* The Unlimited Plan costs $100 per month for as many minutes as you care to use.

Size: px
Start display at page:

Download "* The Unlimited Plan costs $100 per month for as many minutes as you care to use."

Transcription

1 Problem: You walk into the new Herizon Wireless store, which just opened in the mall. They offer two different plans for voice (the data and text plans are separate): * The Unlimited Plan costs $100 per month for as many minutes as you care to use. * The Pay-Go Plan costs 30 cents per minute but has no monthly charge. Which types of customers should choose which plan? Introduction to the Solution: To solve this problem we need to calculate which plan is more cost efficient for a customer based on how many minutes they talk per month. To solve this problem mathematically, we first need to set up an equation for each plan. We can use the slope-intercept form, y = mx+b, as a model for each plan s equation. Since we are looking for the cost of each plan based off of how many minutes a customer talks per month, we will let the variable y equal the cost of each plan per month and let the variable x equal how many minutes a customer talks per month. For the Unlimited Plan, the cost is always $100 whether you talk 1,000,000 minutes or 0 minutes. For the Pay-Go Plan, you have no monthly charge but instead you pay 30 cents for each minute you talk. So in order to get the monthly cost on the Pay-Go plan we must multiply how many minutes we talk in a month by 30 cents (.30). So, Equation for Unlimited Plan: Equation for Pay-Go Plan: TI-Nspire Solution: Y Cost of plan & X Minutes talked Y = 100 Y =.30*X Now that we have the equations for both plans we must now find which plan is more cost efficient for how many minutes a customer may talk. One way we can calculate this is by creating a graph using the TI-Nspire CAS app.

2 First we create a graph for the Unlimited Plan, Y = 100. Next, we create the graph for the Pay-Go plan, Y =.30*X We can see in the image above that the graphs intersect. The point at which the graphs intersect is where the X and Y values of each equation are equal. Where these values are equal means that not only are the number of minutes talked equal but so is the price of each plan. We can then use

3 the tool menu, seen as the wrench in the blue bar at the top of each image, to find the point of intersection. First click the wrench, then Analyze Graph in the drop down menu and then the option Intersection. After selecting Intersection a vertical line will appear on the graph representing the lower bound. After placing the lower bound at its desired point we then can drag the upper bound over the point of intersection in order for the app to give us our intersection point. We can then see that the intersection point of the two equations lies at (333,100). This means at 333 minutes both plans will cost $100.

4 By analyzing the graphs we can also notice that for every x-value less than 333 the y-values for the Pay-Go Plan (f2) graph are less than they y-values for the Unlimited Plan (f1). This means for any amount of minutes less than 333 the Pay-Go plan is going to be cheaper. Also, for every x-value greater than 333 the y-values for the Pay-Go plan are greater than the y-values of the Unlimited Plan. This means for any amount of minutes greater than 333 the Pay-Go Plan is going to more expensive than the Unlimited Plan. Through this data we can then advise a customer which plan they should choose based on how many minutes they talk each month. This can also be represented by the following inequality: Pay-Go Plan 333 Minutes Unlimited Plan If a customer talks less than 333 minutes per month then they should choose the Pay-Go Plan and if they talk more than 333 minutes per month they should choose the Unlimited Plan. Now, if they talk exactly 333 minutes a month the plan will both cost $100, so either plan will be fine. However, Herizon advises they better not risk it and just go for the Unlimited Plan. Problem Continued: In response to popular demand, Herizon decided to offer a new plan that combines the best of their two existing plans: * The Select Plan only costs $40 per month and you pay only 13 cents per minute. Which types of customers should switch to the new plan? TI-Nspire Solution Continued: We now have another plan to take into account when it comes to advising customers in which plan to choose. As we did for the previous two plans we must also create an equation for the Select Plan. Again, we will use the slope-intercept form, y = mx+b, as a model. The y-value will again represent the cost of the plan and the x-value will represent the number of minutes talked.

5 However, the Select Plan has a regular monthly cost of $40 regardless of how many minutes you talk, plus an addition 13 cents (.13) for each minute you talk. Equation for Select Plan: Y =.13*X + 40 The.13*X represents the price for how many minutes you talk and the 40 represents the charge for each month of service. So, if a customer talks for 100 minutes one month their phone bill will be = $ We can now add the Select Plan s equation to the graph and repeat our steps we used in the first part of the problem to find which customers should choose the Select Plan. We create the graph for the Select Plan, Y =.13*X We can now visualize the Select Plan s graph (f3) intersecting both of Herizon s other plan s graphs. Next, we will repeat the same process we used before in order to find our two new intersection points. First, select the wrench, then select Analyze Graph, and lastly Intersection. We then set our lower and upper bounds so the intersection point lies between them in order to find the exact intersection point.

6 After finding our two new intersection points we see that the Select Plan intersects the Pay-Go Plan at the point (235, 70.6). We also see that it intersects the Unlimited Plan at the point (462, 100). By further analyzing the graph we can see that the y-values for the Pay-Go Plan (f1) are less than the y-values of the Select Plan (f3) and the Unlimited Plan (f1) for all x-values less than 235. This means that for all minute values less than 235 the Pay-Go Plan will be the least expensive. We also notice that for the x-values between 235 and 462 the y-values are the least for the Select Plan (f3). Lastly, for all x-values greater than 462 the y-values are the least for the Unlimited Plan (f1). We can express the new data by the following inequality: Pay-Go Plan 235 Minutes Select Plan 462 Minutes Unlimited Plan This inequality states that if a customer talks less than 235 minutes per month they should stick with the Pay-Go plan. If a customer talks between 235 minutes and 462 minutes per month they should choose the new Select Plan. If the customer is a Chatty Cathy and talks more than 462 minutes per month they should select the Unlimited Plan. Microsoft Excel Solution: Not only can we solve this problem by using graphs and calculators but we can also solve it using spreadsheets such as Microsoft Excel. Excel is great for analyzing large amounts of data. Using Excel we can calculate and see how much each plan will cost side by side for any given value of minutes a customer may talk. We start our spreadsheet by creating a column for the minutes and each of the three plans we were given. We then want to create a large list of minute values to analyze the cost of each plan at those values. We ll start at zero and increase by increments of 5. To do so, we start by simply typing zero into cell A2. Instead of typing 5 into cell A3 we can create a formula to make the listing process easier.

7 In Excel we can create formulas by using the names of cells that we may want to build off of. Here we want to get a list of minutes in increments of 5. To get 5 in cell A3 we type =A2+5 into the box f(x). The equals sign is very important and if left out Excel will not calculate the following cell. Now that we have the formula that gives us 5 we can then use another handy tool Excel offers instead of typing =A3+5 into the cell A4. By clicking and dragging the small black box in the lower left hand corner we can apply our created formula to the following cells. This tool is called fill down. To get a larger amount of minute values we will fill these columns all the way down to row 100. Next we need to create the formula for the Unlimited Plan. Our formula we create for the Unlimited Plan was Y = 100. So no matter how many minutes a customer may use the cost of the Unlimited Plan will always be $100. We simply type in 100 into cell B2. We then apply the fill down tool directly from this cell all the way to B100 to get 100 into each cell in column B.

8 Next we need to create our values for the Pay-Go Plan. The Pay-Go Plan costs 30 cents per minute and the formula to calculate its cost is Y =.30*X. Instead of using x we want to use the corresponding minute value in column A. To get our value of the Pay-Go Plan for the minute value of 0 we type in the f(x) box, =.3*A2. To make our job easier we then use the fill down tool again and drag the C column all the way to row 100.

9 After we fill down we can click on any given cell and check our f(x) box to make sure our formulas are working. As seen in the image above, clicking on cell C4 shows that it calculated the cost using the minute value in A4 as it should. We then repeat this same process for our Select Plan column using its equation y =.13*x+40. As we did for the Pay-Go Plan we use the cells in column A instead of x as seen in the f(x) box. Again, we fill down all the way to row 100. For the sake of space, here is an example of what the spreadsheet should now look like for minute values up to 80.

10 To solve the problem, we need to analyze the table and see what plan is cheapest for the range of minutes. If we look at the start of the table we see that the Pay-Go Plan is the cheapest for the lower minute values. As we scroll down we notice that between rows 49 and 50 the Select Plan becomes cheaper than the Pay-Go Plan. However, since we increased our minutes by increments of 5 we don t exactly where the Select Plan becomes cheaper. In order to do so we need to create another table. This time we will start our minute s column at 235 and increase them by a value of 0.1.

11 As we see in the image about the Select Plan becomes cheaper than the Pay-Go plan at a minute value of As you may have noticed this value is more accurate than the one given in TI- Nspire. However, cell phone companies such as Herizon Wireless aren t that generous and always round up to the next whole minute value. So, if you have the Pay-Go plan and talk for minutes you will be charged as if you talked for 236 minutes. We can use an inequality again to express which plan customers should pick: Pay-Go < 235 Minutes < Select This inequality represents the fact that if a customer talks less than 235 minutes they should choose the Pay-Go plan and if the talk more than that they should choose the Select Plan. However, we also notice that the Select plan is still increasing and the Unlimited Plan stays at 100 so we continue to scroll down to see if the Select Plan becomes more expansive than the Unlimited Plan. Again, we notice that somewhere between row 94 and 95 the Select Plan becomes more expensive than the Unlimited Plan. We now need to decrease the increments in which the minutes increase to see exactly where it becomes more expensive.

12 By changing the minutes to increase by.1 again instead of 5 we get a more accurate representation. By analyzing this graph we notice that the select plan becomes more expensive at the minute value of But remember, Herizon always rounds up to the next whole minute value. By creating another inequality we get: Select Plan < 462 Minutes < Unlimited Plan So if a customer talks more than 462 minutes they should then go with the unlimited plan for the better deal. When we add this new inequality to the previous one we get: Pay-Go Plan < 235 Minutes < Select Plan < 462 Minutes < Unlimited Plan By comparing our answer from Excel to TI-Nspire we notice all the same except one difference. The signs in the inequality are less than as opposed to less than or equal to. As we noticed in our more accurate table the Pay-Go and Select Plans were not equal at 235 minutes, the Select Plan was 5 cents more. In final conclusion, since Herizon Wireless always rounds up to the next whole minute value, if a customer talks less than 235 minutes they should choose the Pay-Go Plan. If the talk between 235 and 462 minutes they should choose the Select Plan and if they talk more than 462 minutes they should go with the Unlimited Plan. Teacher Discussion: This activity addresses a number of standards in the Alabama Course of Study, particularly at the 7 th and 8 th grade levels. For the 7 th grade level the activity addresses standards 7-EE4 and 7- EE4a.

13 Standard 7-EE4 states: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Standard 7-EE4a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. In this cellphone example we used these standards in the introduction where the formulas for the cellphone plans were created. We let the variables x and y represent minutes and cost respectively and used formulas similar to the format px + q = r. The activity also met the standards 8-EE7(a) and 8-EE8(a,b,c). Standard 8-EE7: Solve linear equations in one variable. Standard 8-EE7a: Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers). This standard particularly applies to the equation of the Unlimited Plan in which y = 100. It did not depend on any value of x and always remained equal to 100. Standard 8-EE8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersections of their graphs because points of intersection satisfy both equations simultaneously. This applied directly to one of the main ideas used in the TI-Nspire solution. We found where each plan was more or less expensive by evaluating the graph before and after the intersection points. Standard 8-EE8b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. This standard was used as the main approach in the TI-Nspire solution. We created graphs of the three plans and analyzed them to come to our solution. Standard 8-EE8c: Solve real world mathematical problems leading to two linear equations in two variables. This standard was met in the problem itself. Although the problem could be expressed completely algebraically, it was stated in a real world approach that applied it to picking out a

14 cellphone plan that was cost efficient for a type of customer. These types of problems answer the question When am I ever going to use this? The activity also met Standard 8-F2: Compare properties of two functions, each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). In the activity we used both graphs and tables, in the form of spreadsheets, to compare the costs of each of the three plans based on how many minutes a customer uses. This activity could be used most effectively in an 8 th grade algebra class. It is great for learning what algebraic formulas can represent, in this case, the cost of a cellphone bill. The activity can be used as a direct answer for the question When will we ever use this? By using the technologies such as TI-Nspire and Excel the students are able to not only come to an answer to the problem but visualize why that answer is the right one. They are also able to visualize and understand why the wrong answer is wrong. This particularly satisfies the Technology Principle and the fact that technology enhances mathematics learning. The students are able to see answers for large amounts of values quickly, as we did in the spreadsheet, without having to do countless numbers of problems which take up lots of time just to see more data. Overall, the activity was extremely successful in solving linear equations and teaching the students how to represent linear equations and what their representations mean, especially when multiple equations are placed on a graph or table together.

Linear Modeling Business 5 Supply and Demand

Linear Modeling Business 5 Supply and Demand Linear Modeling Business 5 Supply and Demand Supply and demand is a fundamental concept in business. Demand looks at the Quantity (Q) of a product that will be sold with respect to the Price (P) the product

More information

Spreadsheet Directions

Spreadsheet Directions The Best Summer Job Offer Ever! Spreadsheet Directions Before beginning, answer questions 1 through 4. Now let s see if you made a wise choice of payment plan. Complete all the steps outlined below in

More information

You should already have a worksheet with the Basic Plus Plan details in it as well as another plan you have chosen from ehealthinsurance.com.

You should already have a worksheet with the Basic Plus Plan details in it as well as another plan you have chosen from ehealthinsurance.com. In earlier technology assignments, you identified several details of a health plan and created a table of total cost. In this technology assignment, you ll create a worksheet which calculates the total

More information

$0.00 $0.50 $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 $4.00 Price

$0.00 $0.50 $1.00 $1.50 $2.00 $2.50 $3.00 $3.50 $4.00 Price Orange Juice Sales and Prices In this module, you will be looking at sales and price data for orange juice in grocery stores. You have data from 83 stores on three brands (Tropicana, Minute Maid, and the

More information

Technology Assignment Calculate the Total Annual Cost

Technology Assignment Calculate the Total Annual Cost In an earlier technology assignment, you identified several details of two different health plans. In this technology assignment, you ll create a worksheet which calculates the total annual cost of medical

More information

TABLE OF CONTENTS C ORRELATION EXPLAINED INTRODUCTION...2 CORRELATION DEFINED...3 LENGTH OF DATA...5 CORRELATION IN MICROSOFT EXCEL...

TABLE OF CONTENTS C ORRELATION EXPLAINED INTRODUCTION...2 CORRELATION DEFINED...3 LENGTH OF DATA...5 CORRELATION IN MICROSOFT EXCEL... Margined Forex trading is a risky form of investment. As such, it is only suitable for individuals aware of and capable of handling the associated risks. Funds in an account traded at maximum leverage

More information

Lesson Multi-Step Inequalities with Distributive Property

Lesson Multi-Step Inequalities with Distributive Property Lesson: Lesson 6..6 Multi-Step Inequalities with Distributive Property 6..6 (Day ) - Supplement Multi-Step Inequalities with Distributive Property Teacher Lesson Plan CC Standards 7.EE.4b Use variables

More information

MLC at Boise State Polynomials Activity 2 Week #3

MLC at Boise State Polynomials Activity 2 Week #3 Polynomials Activity 2 Week #3 This activity will discuss rate of change from a graphical prespective. We will be building a t-chart from a function first by hand and then by using Excel. Getting Started

More information

MATH THAT MAKES ENTS

MATH THAT MAKES ENTS On December 31, 2012, Curtis and Bill each had $1000 to start saving for retirement. The two men had different ideas about the best way to save, though. Curtis, who doesn t trust banks, put his money in

More information

Algebra I EOC 10-Day STAAR Review. Hedgehog Learning

Algebra I EOC 10-Day STAAR Review. Hedgehog Learning Algebra I EOC 10-Day STAAR Review Hedgehog Learning Day 1 Day 2 STAAR Reporting Category Number and Algebraic Methods Readiness Standards 60% - 65% of STAAR A.10(E) - factor, if possible, trinomials with

More information

GOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16.

GOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16. MA109 College Algebra Fall 017 Exam 017-10-18 Name: Sec.: Do not remove this answer page you will turn in the entire exam. You have two hours to do this exam. No books or notes may be used. You may use

More information

Mathematics Success Grade 8

Mathematics Success Grade 8 Mathematics Success Grade 8 T379 [OBJECTIVE] The student will derive the equation of a line and use this form to identify the slope and y-intercept of an equation. [PREREQUISITE SKILLS] Slope [MATERIALS]

More information

YEAR 12 Trial Exam Paper FURTHER MATHEMATICS. Written examination 1. Worked solutions

YEAR 12 Trial Exam Paper FURTHER MATHEMATICS. Written examination 1. Worked solutions YEAR 12 Trial Exam Paper 2018 FURTHER MATHEMATICS Written examination 1 Worked solutions This book presents: worked solutions explanatory notes tips on how to approach the exam. This trial examination

More information

To compare the different growth patterns for a sum of money invested under a simple interest plan and a compound interest plan.

To compare the different growth patterns for a sum of money invested under a simple interest plan and a compound interest plan. Student Activity 7 8 9 10 11 12 Aim TI-Nspire CAS Investigation Student 180min To compare the different growth patterns for a sum of money invested under a simple interest plan and a compound interest

More information

GOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16.

GOOD LUCK! 2. a b c d e 12. a b c d e. 3. a b c d e 13. a b c d e. 4. a b c d e 14. a b c d e. 5. a b c d e 15. a b c d e. 6. a b c d e 16. MA109 College Algebra Spring 2017 Exam2 2017-03-08 Name: Sec.: Do not remove this answer page you will turn in the entire exam. You have two hours to do this exam. No books or notes may be used. You may

More information

An application program that can quickly handle calculations. A spreadsheet uses numbers like a word processor uses words.

An application program that can quickly handle calculations. A spreadsheet uses numbers like a word processor uses words. An application program that can quickly handle calculations A spreadsheet uses numbers like a word processor uses words. WHAT IF? Columns run vertically & are identified by letters A, B, etc. Rows run

More information

Final Project. College Algebra. Upon successful completion of this course, the student will be able to:

Final Project. College Algebra. Upon successful completion of this course, the student will be able to: COURSE OBJECTIVES Upon successful completion of this course, the student will be able to: 1. Perform operations on algebraic expressions 2. Perform operations on functions expressed in standard function

More information

Before How can lines on a graph show the effect of interest rates on savings accounts?

Before How can lines on a graph show the effect of interest rates on savings accounts? Compound Interest LAUNCH (7 MIN) Before How can lines on a graph show the effect of interest rates on savings accounts? During How can you tell what the graph of simple interest looks like? After What

More information

EconS Constrained Consumer Choice

EconS Constrained Consumer Choice EconS 305 - Constrained Consumer Choice Eric Dunaway Washington State University eric.dunaway@wsu.edu September 21, 2015 Eric Dunaway (WSU) EconS 305 - Lecture 12 September 21, 2015 1 / 49 Introduction

More information

Mathematics Success Level H

Mathematics Success Level H Mathematics Success Level H T473 [OBJECTIVE] The student will graph a line given the slope and y-intercept. [MATERIALS] Student pages S160 S169 Transparencies T484, T486, T488, T490, T492, T494, T496 Wall-size

More information

Math of Finance Exponential & Power Functions

Math of Finance Exponential & Power Functions The Right Stuff: Appropriate Mathematics for All Students Promoting the use of materials that engage students in meaningful activities that promote the effective use of technology to support mathematics,

More information

MLC at Boise State Polynomials Activity 3 Week #5

MLC at Boise State Polynomials Activity 3 Week #5 Polynomials Activity 3 Week #5 This activity will be discuss maximums, minimums and zeros of a quadratic function and its application to business, specifically maximizing profit, minimizing cost and break-even

More information

Expectation Exercises.

Expectation Exercises. Expectation Exercises. Pages Problems 0 2,4,5,7 (you don t need to use trees, if you don t want to but they might help!), 9,-5 373 5 (you ll need to head to this page: http://phet.colorado.edu/sims/plinkoprobability/plinko-probability_en.html)

More information

Personal Finance Amortization Table. Name: Period:

Personal Finance Amortization Table. Name: Period: Personal Finance Amortization Table Name: Period: Ch 8 Project using Excel In this project you will complete a loan amortization table (payment schedule) for the purchase of a home with a $235,500 loan

More information

Creating a Rolling Income Statement

Creating a Rolling Income Statement Creating a Rolling Income Statement This is a demonstration on how to create an Income Statement that will always return the current month s data as well as the prior 12 months data. The report will be

More information

Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Correlated to: Minnesota K-12 Academic Standards in Mathematics, 9/2008 (Grade 7)

Prentice Hall Connected Mathematics 2, 7th Grade Units 2009 Correlated to: Minnesota K-12 Academic Standards in Mathematics, 9/2008 (Grade 7) 7.1.1.1 Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but that it can be approximated by rational

More information

Student Guide: RWC Simulation Lab. Free Market Educational Services: RWC Curriculum

Student Guide: RWC Simulation Lab. Free Market Educational Services: RWC Curriculum Free Market Educational Services: RWC Curriculum Student Guide: RWC Simulation Lab Table of Contents Getting Started... 4 Preferred Browsers... 4 Register for an Account:... 4 Course Key:... 4 The Student

More information

Piecewise-Defined Functions

Piecewise-Defined Functions The Right Stuff: Appropriate Mathematics for All Students Promoting materials that engage students in meaningful activities, promote the effective use of technology to support the mathematics, further

More information

Introduction to Basic Excel Functions and Formulae Note: Basic Functions Note: Function Key(s)/Input Description 1. Sum 2. Product

Introduction to Basic Excel Functions and Formulae Note: Basic Functions Note: Function Key(s)/Input Description 1. Sum 2. Product Introduction to Basic Excel Functions and Formulae Excel has some very useful functions that you can use when working with formulae. This worksheet has been designed using Excel 2010 however the basic

More information

The Advanced Budget Project Part D The Budget Report

The Advanced Budget Project Part D The Budget Report The Advanced Budget Project Part D The Budget Report A budget is probably the most important spreadsheet you can create. A good budget will keep you focused on your ultimate financial goal and help you

More information

Page Points Score Total: 100

Page Points Score Total: 100 Math 1130 Spring 2019 Sample Midterm 3a 4/11/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 9 pages (including this cover page) and 9 problems. Check to see if any

More information

Section 9.1 Solving Linear Inequalities

Section 9.1 Solving Linear Inequalities Section 9.1 Solving Linear Inequalities We know that a linear equation in x can be expressed as ax + b = 0. A linear inequality in x can be written in one of the following forms: ax + b < 0, ax + b 0,

More information

Budget Estimator Tool & Budget Template

Budget Estimator Tool & Budget Template Budget Estimator Tool & Budget Template Integrated Refugee and Immigrant Services Created for you by a Yale School of Management student team IRIS BUDGET TOOLS 1 IRIS Budget Estimator and Budget Template

More information

Jacob: What data do we use? Do we compile paid loss triangles for a line of business?

Jacob: What data do we use? Do we compile paid loss triangles for a line of business? PROJECT TEMPLATES FOR REGRESSION ANALYSIS APPLIED TO LOSS RESERVING BACKGROUND ON PAID LOSS TRIANGLES (The attached PDF file has better formatting.) {The paid loss triangle helps you! distinguish between

More information

Laboratory I.9 Applications of the Derivative

Laboratory I.9 Applications of the Derivative Laboratory I.9 Applications of the Derivative Goals The student will determine intervals where a function is increasing or decreasing using the first derivative. The student will find local minima and

More information

Cost (in dollars) 0 (free) Number of magazines purchased

Cost (in dollars) 0 (free) Number of magazines purchased Math 1 Midterm Review Name *****Don t forget to study the other methods for solving systems of equations (substitution and elimination) as well as systems of linear inequalities and line of best fit! Also,

More information

The Best Cell Phone Plan

The Best Cell Phone Plan Overview Activity ID: 8605 Math Concepts Materials Students will compare two cell phone plans and determine linear functions TI-30XS which plan is better for a specific situation. They will utilize graphing

More information

Buying A Car. Mathematics Capstone Course

Buying A Car. Mathematics Capstone Course Buying A Car Mathematics Capstone Course I. UNIT OVERVIEW & PURPOSE: In this lesson the student will be asked to search the Internet and find a car that he/she would like to purchase. The student will

More information

Applications of Exponential Functions Group Activity 7 Business Project Week #10

Applications of Exponential Functions Group Activity 7 Business Project Week #10 Applications of Exponential Functions Group Activity 7 Business Project Week #10 In the last activity we looked at exponential functions. This week we will look at exponential functions as related to interest

More information

Review Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such.

Review Exercise Set 13. Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Review Exercise Set 13 Exercise 1: Find the slope and the equation of the line in the following graph. If the slope is undefined, then indicate it as such. Exercise 2: Write a linear function that can

More information

Page Points Score Total: 100

Page Points Score Total: 100 Math 1130 Spring 2019 Sample Midterm 2b 2/28/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 10 pages (including this cover page) and 9 problems. Check to see if any

More information

Math Performance Task Teacher Instructions

Math Performance Task Teacher Instructions Math Performance Task Teacher Instructions Stock Market Research Instructions for the Teacher The Stock Market Research performance task centers around the concepts of linear and exponential functions.

More information

Exponential & Logarithmic

Exponential & Logarithmic Exponential & Logarithmic Frank C. Wilson Functions I by file Activity Collection m Credit Card Balance Transfer DVD Player Sales Government Employee Salaries Living Longer Low Interest or Cash Back Shopping

More information

Math 1314 Week 6 Session Notes

Math 1314 Week 6 Session Notes Math 1314 Week 6 Session Notes A few remaining examples from Lesson 7: 0.15 Example 17: The model Nt ( ) = 34.4(1 +.315 t) gives the number of people in the US who are between the ages of 45 and 55. Note,

More information

Survey of Math: Chapter 21: Consumer Finance Savings (Lecture 1) Page 1

Survey of Math: Chapter 21: Consumer Finance Savings (Lecture 1) Page 1 Survey of Math: Chapter 21: Consumer Finance Savings (Lecture 1) Page 1 The mathematical concepts we use to describe finance are also used to describe how populations of organisms vary over time, how disease

More information

How Much Money Should Dr. Evil Demand?

How Much Money Should Dr. Evil Demand? robertkaplinsky.com http://robertkaplinsky.com/work/dr-evil/ How Much Money Should Dr. Evil Demand? The Situation The Challenge(s) How much money should Dr. Evil demand? What would the inflation rate have

More information

Computing compound interest and composition of functions

Computing compound interest and composition of functions Computing compound interest and composition of functions In today s topic we will look at using EXCEL to compute compound interest. The method we will use will also allow us to discuss composition of functions.

More information

January 29. Annuities

January 29. Annuities January 29 Annuities An annuity is a repeating payment, typically of a fixed amount, over a period of time. An annuity is like a loan in reverse; rather than paying a loan company, a bank or investment

More information

I(g) = income from selling gearboxes C(g) = cost of purchasing gearboxes The BREAK-EVEN PT is where COST = INCOME or C(g) = I(g).

I(g) = income from selling gearboxes C(g) = cost of purchasing gearboxes The BREAK-EVEN PT is where COST = INCOME or C(g) = I(g). Page 367 I(g) = income from selling gearboxes C(g) = cost of purchasing gearboxes The BREAK-EVEN PT is where COST = INCOME or C(g) = I(g). PROFIT is when INCOME > COST or I(g) > C(g). I(g) = 8.5g g = the

More information

starting on 5/1/1953 up until 2/1/2017.

starting on 5/1/1953 up until 2/1/2017. An Actuary s Guide to Financial Applications: Examples with EViews By William Bourgeois An actuary is a business professional who uses statistics to determine and analyze risks for companies. In this guide,

More information

WEB APPENDIX 8A 7.1 ( 8.9)

WEB APPENDIX 8A 7.1 ( 8.9) WEB APPENDIX 8A CALCULATING BETA COEFFICIENTS The CAPM is an ex ante model, which means that all of the variables represent before-the-fact expected values. In particular, the beta coefficient used in

More information

Unit 1 Maths Methods (CAS) Exam 2013 Thursday June 6th pm

Unit 1 Maths Methods (CAS) Exam 2013 Thursday June 6th pm Name: Teacher: Unit 1 Maths Methods (CAS) Exam 2013 Thursday June 6th 1.50-3.20 pm Reading time: 10 Minutes Writing time: 80 Minutes Instruction to candidates: Students are permitted to bring into the

More information

Optimization Methods in Management Science

Optimization Methods in Management Science Problem Set Rules: Optimization Methods in Management Science MIT 15.053, Spring 2013 Problem Set 6, Due: Thursday April 11th, 2013 1. Each student should hand in an individual problem set. 2. Discussing

More information

Page Points Score Total: 100

Page Points Score Total: 100 Math 1130 Autumn 2018 Sample Midterm 2c 2/28/19 Name (Print): Username.#: Lecturer: Rec. Instructor: Rec. Time: This exam contains 8 pages (including this cover page) and 6 problems. Check to see if any

More information

(GPA, student) (area code, person) (person, shirt color)

(GPA, student) (area code, person) (person, shirt color) Foundations of Algebra Unit 5 Review Part One Name: Day One: Function Notation In order for a relation to be a function, every must have exactly one. 1) Determine whether each of the following represents

More information

Using the Budget Features in Quicken 2003

Using the Budget Features in Quicken 2003 Using the Budget Features in Quicken 2003 Quicken budgets can be used to summarize expected income and expenses for planning purposes. The budget can later be used in comparisons to actual income and expenses

More information

Cell Phone Plans Assignment

Cell Phone Plans Assignment Cell Phone Plans Assignment Name: /43 Total This Investigation has the following components: INTRODUCTION Overview of the different Plans PART A Make a hypothesis à which do you think is best for you (2

More information

Computing interest and composition of functions:

Computing interest and composition of functions: Computing interest and composition of functions: In this week, we are creating a simple and compound interest calculator in EXCEL. These two calculators will be used to solve interest questions in week

More information

4.5 Comparing Exponential Functions

4.5 Comparing Exponential Functions 4.5 Comparing Exponential Functions So far we have talked in detail about both linear and exponential functions. In this section we ll compare exponential functions to other exponential functions and also

More information

The Expenditure-Output

The Expenditure-Output The Expenditure-Output Model By: OpenStaxCollege (This appendix should be consulted after first reading The Aggregate Demand/ Aggregate Supply Model and The Keynesian Perspective.) The fundamental ideas

More information

Copyright 2011 Pearson Education, Inc. Publishing as Addison-Wesley.

Copyright 2011 Pearson Education, Inc. Publishing as Addison-Wesley. Appendix: Statistics in Action Part I Financial Time Series 1. These data show the effects of stock splits. If you investigate further, you ll find that most of these splits (such as in May 1970) are 3-for-1

More information

Quadratic Modeling Elementary Education 10 Business 10 Profits

Quadratic Modeling Elementary Education 10 Business 10 Profits Quadratic Modeling Elementary Education 10 Business 10 Profits This week we are asking elementary education majors to complete the same activity as business majors. Our first goal is to give elementary

More information

Section 4.3 Objectives

Section 4.3 Objectives CHAPTER ~ Linear Equations in Two Variables Section Equation of a Line Section Objectives Write the equation of a line given its graph Write the equation of a line given its slope and y-intercept Write

More information

Project your expenses

Project your expenses Welcome to the Victory Cashflow worksheet. Spending just half an hour each month will ensure your budget is maintained and your finances are in order. The objective of this budget is to predict the future

More information

BikeRite Kickstarter Campaign

BikeRite Kickstarter Campaign BikeRite Kickstarter Campaign Background Kickstarter (http://www.kickstarter.com/) is a popular crowdfunding site that was launched in 2009. Kickstarter was originally conceived to help artists raise funds

More information

HandDA program instructions

HandDA program instructions HandDA program instructions All materials referenced in these instructions can be downloaded from: http://www.umass.edu/resec/faculty/murphy/handda/handda.html Background The HandDA program is another

More information

SAMPLE. Financial arithmetic

SAMPLE. Financial arithmetic C H A P T E R 6 Financial arithmetic How do we determine the new price when discounts or increases are applied? How do we determine the percentage discount or increase applied, given the old and new prices?

More information

Using an Excel spreadsheet to calculate Andrew s 18th birthday costs

Using an Excel spreadsheet to calculate Andrew s 18th birthday costs Using an Excel spreadsheet to calculate Andrew s 18th birthday costs Open a new spreadsheet in Excel. Highlight cells A1 to J1. Prevocational Mathematics 1 of 17 Planning an event Using an Excel spreadsheet

More information

6.3 Comparing Functions

6.3 Comparing Functions ? LESSN 6.3 Comparing Functions ESSENTIAL QUESTIN How can you use tables, graphs, and equations to compare functions? Proportionality 8.5.I Write an equation in the form y = mx + b to model a linear relationship

More information

Pearson Connected Mathematics Grade 7

Pearson Connected Mathematics Grade 7 A Correlation of Pearson Connected Mathematics 2 2012 to the Common Core Georgia Performance s Grade 7 FORMAT FOR CORRELATION TO THE COMMON CORE GEORGIA PERFORMANCE STANDARDS (CCGPS) Subject Area: K-12

More information

Frequency Distributions

Frequency Distributions Frequency Distributions January 8, 2018 Contents Frequency histograms Relative Frequency Histograms Cumulative Frequency Graph Frequency Histograms in R Using the Cumulative Frequency Graph to Estimate

More information

Comparing Linear Increase and Exponential Growth

Comparing Linear Increase and Exponential Growth Lesson 7-7 Comparing Linear Increase and Exponential Growth Lesson 7-7 BIG IDEA In the long run, exponential growth always overtakes linear (constant) increase. In the patterns that are constant increase/decrease

More information

= quantity of ith good bought and consumed. It

= quantity of ith good bought and consumed. It Chapter Consumer Choice and Demand The last chapter set up just one-half of the fundamental structure we need to determine consumer behavior. We must now add to this the consumer's budget constraint, which

More information

Decision Trees: Booths

Decision Trees: Booths DECISION ANALYSIS Decision Trees: Booths Terri Donovan recorded: January, 2010 Hi. Tony has given you a challenge of setting up a spreadsheet, so you can really understand whether it s wiser to play in

More information

Name Name. To enter the data manually, go to the StatCrunch website (www.statcrunch.com) and log in (new users must register).

Name Name. To enter the data manually, go to the StatCrunch website (www.statcrunch.com) and log in (new users must register). Chapter 5 Project: Broiler Chicken Production Name Name 1. Background information The graph and data that form the basis of this project were taken from a very useful web site sponsored by the National

More information

Student Activity: Show Me the Money!

Student Activity: Show Me the Money! 1.2 The Y-Intercept: Student Activity Student Activity: Show Me the Money! Overview: Objective: Terms: Materials: Procedures: Students connect recursive operations with graphs. Algebra I TEKS b.3.b Given

More information

Master Budget Excel Project

Master Budget Excel Project Master Budget Excel Project Overview: In this project, you will prepare a master budget in an Excel spreadsheet for Cascade Products Company for the year 2018, based on the materials in Ch. 7 Master Budgeting.

More information

BARUCH COLLEGE MATH 2003 SPRING 2006 MANUAL FOR THE UNIFORM FINAL EXAMINATION

BARUCH COLLEGE MATH 2003 SPRING 2006 MANUAL FOR THE UNIFORM FINAL EXAMINATION BARUCH COLLEGE MATH 003 SPRING 006 MANUAL FOR THE UNIFORM FINAL EXAMINATION The final examination for Math 003 will consist of two parts. Part I: Part II: This part will consist of 5 questions similar

More information

Chapter 6: Supply and Demand with Income in the Form of Endowments

Chapter 6: Supply and Demand with Income in the Form of Endowments Chapter 6: Supply and Demand with Income in the Form of Endowments 6.1: Introduction This chapter and the next contain almost identical analyses concerning the supply and demand implied by different kinds

More information

Every data set has an average and a standard deviation, given by the following formulas,

Every data set has an average and a standard deviation, given by the following formulas, Discrete Data Sets A data set is any collection of data. For example, the set of test scores on the class s first test would comprise a data set. If we collect a sample from the population we are interested

More information

Form 162. Form 194. Form 239

Form 162. Form 194. Form 239 Below is a list of topics that we receive calls about each year with the solutions to them detailed. New features and funds have also been added. Note: Some of the topics have more than one question so

More information

more information Upload a contribution file

more information Upload a contribution file Upload a contribution file more information About the Microsoft Excel contribution process Upload a contribution file is an online process that allows you to submit Microsoft Excel (Excel) contribution

More information

Lesson 28. Student Outcomes. Lesson Notes. Materials. Classwork. Formulating the Problem (15 minutes)

Lesson 28. Student Outcomes. Lesson Notes. Materials. Classwork. Formulating the Problem (15 minutes) Student Outcomes Students create equations and inequalities in one variable and use them to solve problems. Students create equations in two or more variables to represent relationships between quantities

More information

THE COST VOLUME PROFIT APPROACH TO DECISIONS

THE COST VOLUME PROFIT APPROACH TO DECISIONS C H A P T E R 8 THE COST VOLUME PROFIT APPROACH TO DECISIONS I N T R O D U C T I O N This chapter introduces the cost volume profit (CVP) method, which can assist management in evaluating current and future

More information

Solutions for practice questions: Chapter 15, Probability Distributions If you find any errors, please let me know at

Solutions for practice questions: Chapter 15, Probability Distributions If you find any errors, please let me know at Solutions for practice questions: Chapter 15, Probability Distributions If you find any errors, please let me know at mailto:msfrisbie@pfrisbie.com. 1. Let X represent the savings of a resident; X ~ N(3000,

More information

MLC at Boise State Lines and Rates Activity 1 Week #2

MLC at Boise State Lines and Rates Activity 1 Week #2 Lines and Rates Activity 1 Week #2 This activity will use slopes to calculate marginal profit, revenue and cost of functions. What is Marginal? Marginal cost is the cost added by producing one additional

More information

Math 122 Calculus for Business Admin. and Social Sciences

Math 122 Calculus for Business Admin. and Social Sciences Math 122 Calculus for Business Admin. and Social Sciences Instructor: Ann Clifton Name: Exam #1 A July 3, 2018 Do not turn this page until told to do so. You will have a total of 1 hour 40 minutes to complete

More information

FTS Real Time Project: Smart Beta Investing

FTS Real Time Project: Smart Beta Investing FTS Real Time Project: Smart Beta Investing Summary Smart beta strategies are a class of investment strategies based on company fundamentals. In this project, you will Learn what these strategies are Construct

More information

Linear Functions I. Sample file. Activity Collection. Featuring the following real-world contexts: by Frank C.

Linear Functions I. Sample file. Activity Collection.  Featuring the following real-world contexts: by Frank C. Linear Functions I by Frank C. Wilson Activity Collection Featuring the following real-world contexts: Choosing a Cell Phone Plan - T-Mobile Choosing a Cell Phone Plan - Verizon College Graduates Michigan

More information

Survey of Math Chapter 21: Savings Models Handout Page 1

Survey of Math Chapter 21: Savings Models Handout Page 1 Chapter 21: Savings Models Handout Page 1 Growth of Savings: Simple Interest Simple interest pays interest only on the principal, not on any interest which has accumulated. Simple interest is rarely used

More information

WEEK 2 REVIEW. Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5)

WEEK 2 REVIEW. Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5) WEEK 2 REVIEW Straight Lines (1.2) Linear Models (1.3) Intersection Points (1.4) Least Squares (1.5) 1 STRAIGHT LINES SLOPE A VERTICAL line has NO SLOPE. All other lines have a slope given by m = rise

More information

ECO101 PRINCIPLES OF MICROECONOMICS Notes. Consumer Behaviour. U tility fro m c o n s u m in g B ig M a c s

ECO101 PRINCIPLES OF MICROECONOMICS Notes. Consumer Behaviour. U tility fro m c o n s u m in g B ig M a c s ECO101 PRINCIPLES OF MICROECONOMICS Notes Consumer Behaviour Overview The aim of this chapter is to analyse the behaviour of rational consumers when consuming goods and services, to explain how they may

More information

CH 39 CREATING THE EQUATION OF A LINE

CH 39 CREATING THE EQUATION OF A LINE 9 CH 9 CREATING THE EQUATION OF A LINE Introduction S ome chapters back we played around with straight lines. We graphed a few, and we learned how to find their intercepts and slopes. Now we re ready to

More information

ExcelBasics.pdf. Here is the URL for a very good website about Excel basics including the material covered in this primer.

ExcelBasics.pdf. Here is the URL for a very good website about Excel basics including the material covered in this primer. Excel Primer for Finance Students John Byrd, November 2015. This primer assumes you can enter data and copy functions and equations between cells in Excel. If you aren t familiar with these basic skills

More information

Jacob: The illustrative worksheet shows the values of the simulation parameters in the upper left section (Cells D5:F10). Is this for documentation?

Jacob: The illustrative worksheet shows the values of the simulation parameters in the upper left section (Cells D5:F10). Is this for documentation? PROJECT TEMPLATE: DISCRETE CHANGE IN THE INFLATION RATE (The attached PDF file has better formatting.) {This posting explains how to simulate a discrete change in a parameter and how to use dummy variables

More information

Chapter 6 Analyzing Accumulated Change: Integrals in Action

Chapter 6 Analyzing Accumulated Change: Integrals in Action Chapter 6 Analyzing Accumulated Change: Integrals in Action 6. Streams in Business and Biology You will find Excel very helpful when dealing with streams that are accumulated over finite intervals. Finding

More information

Calculate Sums, Rates, and Percentages in Excel: Student Workbook

Calculate Sums, Rates, and Percentages in Excel: Student Workbook 2016 Calculate Sums, Rates, and Percentages in Excel: Student Workbook Created by: EVA CONSTANTARAS / Independent Consultant & Data Scientist WITH SUPPORT FROM THE WORLD BANK AND THE UK DEPARTMENT FOR

More information

Budget Quick-Start Guide. Welcome to the Budget Quick-Start Guide, five simple pages to get you going with

Budget Quick-Start Guide. Welcome to the Budget Quick-Start Guide, five simple pages to get you going with Budget Quick-Start Guide Welcome to the Budget Quick-Start Guide, five simple pages to get you going with the single most powerful, practical tool for wise money management. Using a budget or, as I prefer,

More information

Maximizing Winnings on Final Jeopardy!

Maximizing Winnings on Final Jeopardy! Maximizing Winnings on Final Jeopardy! Jessica Abramson, Natalie Collina, and William Gasarch August 2017 1 Introduction Consider a final round of Jeopardy! with players Alice and Betty 1. We assume that

More information

Algebra Success. LESSON 14: Discovering y = mx + b

Algebra Success. LESSON 14: Discovering y = mx + b T282 Algebra Success [OBJECTIVE] The student will determine the slope and y-intercept of a line by examining the equation for the line written in slope-intercept form. [MATERIALS] Student pages S7 S Transparencies

More information