(i.e. the rate of change of y with respect to x)

Size: px
Start display at page:

Download "(i.e. the rate of change of y with respect to x)"

Transcription

1 Section Linear Functions and Math Models Example 1: Questions we d like to answer: 1. What is the slope of the line? 2. What is the equation of the line? 3. What is the y-intercept? 4. What is the x-intercept? Definition: If (x 1,y 1 ) and (x 2,y 2 ) are two distinct points on a line L, then the slope (m) of L is (i.e. the rate of change of y with respect to x) Answer to Question 1: 1

2 Definition: (Point-Slope Form) The equation of the line that passes through the point (x 1,y 1 ) and has slope m is given by: Definition (Slope-Intercept Form) The equation of the line that has slope m and intersects the y-axis at the point (0,b) is given by: Answer to Question 2: Answer to Question 3: Answer to Question 4: Equations of Special Lines: Horizontal Line: Vertical Line: 2

3 Definition: A function is a rule that assigns to each value of x one and only one value of y. We refer to x as the variable and to y as the variable. The set of all possible values that x can assume is the and the set of all possible values that y can assume is the. We will concentrate on linear functions (those that can be represented graphically by a line) Applications: 1. Linear Depreciation Example 2: In 2009 Texas A&M installed a new machine in one of its departments at a cost of $250,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000. (a) Find an expression for the machine s book value in the tth year of use. (b) Sketch the graph of the function in part (a). (c) Find the machine s book value in (d) Find the rate at which the machine is being depreciated. 3

4 2. Linear Demand and Supply Curves Example 3: At a unit price of $55, the quantity demanded of a certain commodity is 1000 units. At a unit price of $85, the demand drops to 600 units. (a) Given that it is linear, find the demand equation. (b) Sketch the demand curve. (c) What quantity would be demanded if the commodity were free? Example 4: Producers will make 2000 cell phones available when the unit price is $100. At a unit price of $200, 6000 cell phones will be marketed. (a) Given that it is linear, find the supply equation. (b) Sketch the supply curve. (c) What is the unit price when 3,000 cell phones are supplied? 4

5 3. Cost, Revenue, and Profit Functions Cost Function (cost of manufacturing x units of a product) where c is the cost per unit and F is the fixed cost. Revenue Function (revenue realized from selling x units of the product) where s is the selling price. Profit Function Example 5: A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit. (a) What is the cost function? (b) What is the revenue function? (c) What is the profit function? (d) Compute the profit (loss) corresponding to production levels of 12,000 and 20,000 units. Section 1.3 Highly Suggested Homework Problems: 11, 13, 15, 21, 23, 33, 37, 45 5

6 Section 1.4 Intersection of Straight Lines Calculator Steps: Graph the two functions by entering the slope-intercept form of the lines into Y1 and Y2 (These are located under the Y= button). After chosing the appropriate Window, hit GRAPH. Go to CALC which is found by pressing 2nd TRACE. Select option 5: intersect The calculator will prompt you for the first and second curves you want to intersect. The cursor will blink on a function and show the function name in the top left corner of the screen. When it blinks on Y1, press enter and when it blinks on Y2 press ENTER. The calculator will then ask you to guess where the intersection point is located. Use your right and left arrow keys to move to the intersection point and press ENTER. The intersection point will appear at the bottom of the screen. Example 1: Find the point of intersection of the lines y = x + 1 and y = 2x + 4 a) Find the point of intersection algebraically. b) Find the point of intersection using the calculator. 6

7 Applications: 1. Market Equilibrium: The point at which the consumer and supplier agree upon (i.e. the point of intersection of the supply and demand curves) Example 2: If the supply equation is 5x 6p + 14 = 0 and the demand equation is 4x + 3p 59 = 0 where x represents the quantity demanded in units of 1000 and p is the unit price in dollars, find the equilibrium quantity and the equilibrium price. 2. Break-Even Point: The point at which the company suffers neither a loss or gain. (i.e. the point of intersection of the revenue and cost functions) Example 3: A manufacturer of garbage disposals, has a monthly fixed cost of $10,000 and a production cost of $20 for each garbage disposal manufactured. The units sell for $50 each. (a) What is the cost function? (b) What is the revenue function? (c) What is the profit function? 7

8 (d) Sketch the graphs of the cost function and the revenue function and hence find the break-even point graphically. (e) Find the break-even point algebraically. (f) Sketch the graph of the profit function. (g) At what point does the graph of the profit function cross the x-axis? Interpret your result. Section 1.4 Highly Suggested Homework Problems: 3, 9, 13, 21, 25, 27 8

9 Section The Method of Least Squares Example 1: The following table gives the actual high temperature in College Station for a few days in August where x represents the day of the month of August and y represents the temperature in F. x y Use the above model to predict the temperature on August 10th. 9

10 Calculator Steps Enter your x and y values into lists. To do this, hit STAT and select 1: Edit... If you have anything in L1 and L2, cursor up to the name of the list, hit CLEAR and ENTER. Now just enter in your values one at a time by pressing ENTER after each number. To find the regression equation, first hit STAT, cursor right to CALC and select option 4: LinReg(ax+b). To have the calculator automatically store the equation into Y1 press VARS, arrow to Y-Vars, select 1:Function and then select Y1. Note: Your homescreen should say LinReg(ax+b) Y1. Now press ENTER To graph the regression line with data points, first enter the equation of the line into Y1(if you didn t automatically store it there). Then make sure your stat plot is turned on. To do this, hit 2nd Y= and select 1...by pressing ENTER. You can then highlight any of the options you would like. Now press ZOOM and select 9: ZoomStat. You will have a plot of the original data points and the least squares line. Example 2: A manufacturer of electric motors, submitted the accompanying data. The table shows the net sales (in millions of dollars) during a 5 year period: Year Net Sales a) Determine the equation of the least-squares line for these data. (Let x represent the number of years since 1999.) b) Draw a scatter diagram and the least-squares line for these data. c) Use the result obtained in part (a) to predict the net sales for d) When will the net sales reach $500 million? Section 1.5 Highly Suggested Homework Problems: 3, 7, 11 10

Section Linear Functions and Math Models

Section Linear Functions and Math Models Section 1.1 - Linear Functions and Math Models Lines: Four basic things to know 1. The slope of the line 2. The equation of the line 3. The x-intercept 4. The y-intercept 1. Slope: If (x 1, y 1 ) and (x

More information

FINITE MATH LECTURE NOTES. c Janice Epstein 1998, 1999, 2000 All rights reserved.

FINITE MATH LECTURE NOTES. c Janice Epstein 1998, 1999, 2000 All rights reserved. FINITE MATH LECTURE NOTES c Janice Epstein 1998, 1999, 2000 All rights reserved. August 27, 2001 Chapter 1 Straight Lines and Linear Functions In this chapter we will learn about lines - how to draw them

More information

Use the data you collected and plot the points to create scattergrams or scatter plots.

Use the data you collected and plot the points to create scattergrams or scatter plots. Key terms: bivariate data, scatterplot (also called scattergram), correlation (positive, negative, or none as well as strong or weak), regression equation, interpolation, extrapolation, and correlation

More information

Using the TI-83 Statistical Features

Using the TI-83 Statistical Features Entering data (working with lists) Consider the following small data sets: Using the TI-83 Statistical Features Data Set 1: {1, 2, 3, 4, 5} Data Set 2: {2, 3, 4, 4, 6} Press STAT to access the statistics

More information

Graphing Calculator Appendix

Graphing Calculator Appendix Appendix GC GC-1 This appendix contains some keystroke suggestions for many graphing calculator operations that are featured in this text. The keystrokes are for the TI-83/ TI-83 Plus calculators. The

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

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

Statistics TI-83 Usage Handout

Statistics TI-83 Usage Handout Statistics TI-83 Usage Handout This handout includes instructions for performing several different functions on a TI-83 calculator for use in Statistics. The Contents table below lists the topics covered

More information

LINES AND SLOPES. Required concepts for the courses : Micro economic analysis, Managerial economy.

LINES AND SLOPES. Required concepts for the courses : Micro economic analysis, Managerial economy. LINES AND SLOPES Summary 1. Elements of a line equation... 1 2. How to obtain a straight line equation... 2 3. Microeconomic applications... 3 3.1. Demand curve... 3 3.2. Elasticity problems... 7 4. Exercises...

More information

AP Stats: 3B ~ Least Squares Regression and Residuals. Objectives:

AP Stats: 3B ~ Least Squares Regression and Residuals. Objectives: Objectives: INTERPRET the slope and y intercept of a least-squares regression line USE the least-squares regression line to predict y for a given x CALCULATE and INTERPRET residuals and their standard

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

MA 162: Finite Mathematics - Chapter 1

MA 162: Finite Mathematics - Chapter 1 MA 162: Finite Mathematics - Chapter 1 Fall 2014 Ray Kremer University of Kentucky Linear Equations Linear equations are usually represented in one of three ways: 1 Slope-intercept form: y = mx + b 2 Point-Slope

More information

Math Week in Review #1. Perpendicular Lines - slopes are opposite (or negative) reciprocals of each other

Math Week in Review #1. Perpendicular Lines - slopes are opposite (or negative) reciprocals of each other Math 141 Spring 2006 c Heather Ramsey Page 1 Section 1.2 m = y x = y 2 y 1 x 2 x 1 Math 141 - Week in Review #1 Point-Slope Form: y y 1 = m(x x 1 ), where m is slope and (x 1,y 1 ) is any point on the

More information

Activity Two: Investigating Slope and Y-Intercept in the Real World. Number of Tickets Cost 8 $ $11.00 $

Activity Two: Investigating Slope and Y-Intercept in the Real World. Number of Tickets Cost 8 $ $11.00 $ Activity Two: Investigating Slope and Y-Intercept in the Real World Directions: Use what you have learned about the concepts of slope and y-intercept to solve: A. A Day at the Fair You and your friends

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

rise m x run The slope is a ratio of how y changes as x changes: Lines and Linear Modeling POINT-SLOPE form: y y1 m( x

rise m x run The slope is a ratio of how y changes as x changes: Lines and Linear Modeling POINT-SLOPE form: y y1 m( x Chapter 1 Notes 1 (c) Epstein, 013 Chapter 1 Notes (c) Epstein, 013 Chapter1: Lines and Linear Modeling POINT-SLOPE form: y y1 m( x x1) 1.1 The Cartesian Coordinate System A properly laeled set of axes

More information

Math 116: Business Calculus

Math 116: Business Calculus Math 116: Business Calculus Instructor: Colin Clark Spring 2017 Exam 1 - Thursday February 9. 1.1 Slopes and Equations of Lines. 1.2 Linear Functions and Applications. 2.1 Properties of Functions. 2.2

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

Chapter 5 Project: Broiler Chicken Production. Name Name

Chapter 5 Project: Broiler Chicken Production. Name Name 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

MA162: Finite mathematics

MA162: Finite mathematics MA162: Finite mathematics Paul Koester University of Kentucky September 4, 2013 Schedule: First Web Assign assignment due on Friday, September 6 by 6:00 pm. Second Web Assign assignment due on Tuesday,

More information

UNIT 11 STUDY GUIDE. Key Features of the graph of

UNIT 11 STUDY GUIDE. Key Features of the graph of UNIT 11 STUDY GUIDE Key Features of the graph of Exponential functions in the form The graphs all cross the y-axis at (0, 1) The x-axis is an asymptote. Equation of the asymptote is y=0 Domain: Range:

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

TI-83 Plus Workshop. Al Maturo,

TI-83 Plus Workshop. Al Maturo, Solving Equations with one variable. Enter the equation into: Y 1 = x x 6 Y = x + 5x + 3 Y 3 = x 3 5x + 1 TI-83 Plus Workshop Al Maturo, AMATURO@las.ch We shall refer to this in print as f(x). We shall

More information

The instructions on this page also work for the TI-83 Plus and the TI-83 Plus Silver Edition.

The instructions on this page also work for the TI-83 Plus and the TI-83 Plus Silver Edition. The instructions on this page also work for the TI-83 Plus and the TI-83 Plus Silver Edition. The position of the graphically represented keys can be found by moving your mouse on top of the graphic. Turn

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

Lab 10: Optimizing Revenue and Profits (Including Elasticity of Demand)

Lab 10: Optimizing Revenue and Profits (Including Elasticity of Demand) Lab 10: Optimizing Revenue and Profits (Including Elasticity of Demand) There's no doubt that the "bottom line" is the maximization of profit, at least to the CEO and shareholders. However, the sales director

More information

Chap3a Introduction to Exponential Functions. Y = 2x + 4 Linear Increasing Slope = 2 y-intercept = (0,4) f(x) = 3(2) x

Chap3a Introduction to Exponential Functions. Y = 2x + 4 Linear Increasing Slope = 2 y-intercept = (0,4) f(x) = 3(2) x Name Date HW Packet Lesson 3 Introduction to Exponential Functions HW Problem 1 In this problem, we look at the characteristics of Linear and Exponential Functions. Complete the table below. Function If

More information

MATH20330: Optimization for Economics Homework 1: Solutions

MATH20330: Optimization for Economics Homework 1: Solutions MATH0330: Optimization for Economics Homework 1: Solutions 1. Sketch the graphs of the following linear and quadratic functions: f(x) = 4x 3, g(x) = 4 3x h(x) = x 6x + 8, R(q) = 400 + 30q q. y = f(x) is

More information

Ti 83/84. Descriptive Statistics for a List of Numbers

Ti 83/84. Descriptive Statistics for a List of Numbers Ti 83/84 Descriptive Statistics for a List of Numbers Quiz scores in a (fictitious) class were 10.5, 13.5, 8, 12, 11.3, 9, 9.5, 5, 15, 2.5, 10.5, 7, 11.5, 10, and 10.5. It s hard to get much of a sense

More information

Interest Formulas. Simple Interest

Interest Formulas. Simple Interest Interest Formulas You have $1000 that you wish to invest in a bank. You are curious how much you will have in your account after 3 years since banks typically give you back some interest. You have several

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

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

When Is Factoring Used?

When Is Factoring Used? When Is Factoring Used? Name: DAY 9 Date: 1. Given the function, y = x 2 complete the table and graph. x y 2 1 0 1 2 3 1. A ball is thrown vertically upward from the ground according to the graph below.

More information

Analyzing Accumulated Change: More Applications of Integrals & 7.1 Differences of Accumulated Changes

Analyzing Accumulated Change: More Applications of Integrals & 7.1 Differences of Accumulated Changes Chapter 7 Analyzing Accumulated Change: More Applications of Integrals & 7.1 Differences of Accumulated Changes This chapter helps you effectively use your calculatorõs numerical integrator with various

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

Notes on a Basic Business Problem MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W

Notes on a Basic Business Problem MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W Notes on a Basic Business Problem MATH 104 and MATH 184 Mark Mac Lean (with assistance from Patrick Chan) 2011W This simple problem will introduce you to the basic ideas of revenue, cost, profit, and demand.

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

The Normal Probability Distribution

The Normal Probability Distribution 102 The Normal Probability Distribution C H A P T E R 7 Section 7.2 4Example 1 (pg. 71) Finding Area Under a Normal Curve In this exercise, we will calculate the area to the left of 5 inches using a normal

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

Math1090 Midterm 2 Review Sections , Solve the system of linear equations using Gauss-Jordan elimination.

Math1090 Midterm 2 Review Sections , Solve the system of linear equations using Gauss-Jordan elimination. Math1090 Midterm 2 Review Sections 2.1-2.5, 3.1-3.3 1. Solve the system of linear equations using Gauss-Jordan elimination. 5x+20y 15z = 155 (a) 2x 7y+13z=85 3x+14y +6z= 43 x+z= 2 (b) x= 6 y+z=11 x y+

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

Cosumnes River College Principles of Macroeconomics Problem Set 6 Due April 3, 2017

Cosumnes River College Principles of Macroeconomics Problem Set 6 Due April 3, 2017 Spring 2017 Cosumnes River College Principles of Macroeconomics Problem Set 6 Due April 3, 2017 Name: Instructions: Write the answers clearly and concisely on these sheets in the spaces provided. Do not

More information

The Zero Product Law. Standards:

The Zero Product Law. Standards: Objective: Students will be able to (SWBAT) use complex numbers in polynomial identities and equations, in order to (IOT) solve quadratic equations with real coefficient that have complex solutions. Standards:

More information

Name Date. Key Math Concepts

Name Date. Key Math Concepts 2-1 Interpret Scatterplots Key Math Concepts Bivariate data is pairs of numbers, (x,y), that represent variables. Positive correlation: the value of one variable increases as the other increases. Negative

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

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

Chapter 5 Summarizing Bivariate Data

Chapter 5 Summarizing Bivariate Data Chapter 5 Summarizing Bivariate Data 5.0 Introduction In Chapter 5 we address some graphic and numerical descriptions of data when two measures are taken from an individual. In the typical situation we

More information

Economics 102 Homework #7 Due: December 7 th at the beginning of class

Economics 102 Homework #7 Due: December 7 th at the beginning of class Economics 102 Homework #7 Due: December 7 th at the beginning of class Complete all of the problems. Please do not write your answers on this sheet. Show all of your work. 1. The economy starts in long

More information

Topic 4: Analysis of Equilibrium.

Topic 4: Analysis of Equilibrium. Topic 4: Analysis of Equilibrium. Outline: 1. Main ideas. Partial equilibrium. General Equilibrium. Offer curves. Terms of trade. 2. Partial equilibrium analysis of trade. 3. General equilibrium analysis

More information

Aggregate Demand & Aggregate Supply

Aggregate Demand & Aggregate Supply Aggregate Demand The aggregate demand () curve shows the total amounts of goods and services that consumers, businesses, governments, and people in other countries will purchase at each and every price

More information

Chapter 14. Descriptive Methods in Regression and Correlation. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 1

Chapter 14. Descriptive Methods in Regression and Correlation. Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 1 Chapter 14 Descriptive Methods in Regression and Correlation Copyright 2016, 2012, 2008 Pearson Education, Inc. Chapter 14, Slide 1 Section 14.1 Linear Equations with One Independent Variable Copyright

More information

CHAPTER 6. Exponential Functions

CHAPTER 6. Exponential Functions CHAPTER 6 Eponential Functions 6.1 EXPLORING THE CHARACTERISTICS OF EXPONENTIAL FUNCTIONS Chapter 6 EXPONENTIAL FUNCTIONS An eponential function is a function that has an in the eponent. Standard form:

More information

S14 Exponential Growth and Decay (Graphing Calculator or App Needed)

S14 Exponential Growth and Decay (Graphing Calculator or App Needed) 1010 Homework Name S14 Exponential Growth and Decay (Graphing Calculator or App Needed) 1. Without graphing, classify each of the following as increasing or decreasing and find f (0). a. f (x) = 1.5(0.75)

More information

Suggested Solutions to Assignment 3

Suggested Solutions to Assignment 3 ECON 1010C Principles of Macroeconomics Instructor: Sharif F. Khan Department of Economics Atkinson College York University Summer 2005 Suggested Solutions to Assignment 3 Part A Multiple-Choice Questions

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

QUADRATIC. Parent Graph: How to Tell it's a Quadratic: Helpful Hints for Calculator Usage: Domain of Parent Graph:, Range of Parent Graph: 0,

QUADRATIC. Parent Graph: How to Tell it's a Quadratic: Helpful Hints for Calculator Usage: Domain of Parent Graph:, Range of Parent Graph: 0, Parent Graph: How to Tell it's a Quadratic: If the equation's largest exponent is 2 If the graph is a parabola ("U"-Shaped) Opening up or down. QUADRATIC f x = x 2 Domain of Parent Graph:, Range of Parent

More information

How Wealthy Are Europeans?

How Wealthy Are Europeans? How Wealthy Are Europeans? Grades: 7, 8, 11, 12 (course specific) Description: Organization of data of to examine measures of spread and measures of central tendency in examination of Gross Domestic Product

More information

Algebra 1 Unit 3: Writing Equations

Algebra 1 Unit 3: Writing Equations Lesson 8: Making Predictions and Creating Scatter Plots The table below represents the cost of a car over the recent years. Year Cost of a Car (in US dollars) 2000 22,500 2002 26,000 2004 32,000 2006 37,500

More information

Statistics 101: Section L - Laboratory 6

Statistics 101: Section L - Laboratory 6 Statistics 101: Section L - Laboratory 6 In today s lab, we are going to look more at least squares regression, and interpretations of slopes and intercepts. Activity 1: From lab 1, we collected data on

More information

3.3 rates and slope intercept form ink.notebook. October 23, page 103. page 104. page Rates and Slope Intercept Form

3.3 rates and slope intercept form ink.notebook. October 23, page 103. page 104. page Rates and Slope Intercept Form 3.3 rates and slope intercept form ink.notebook page 103 page 104 page 102 3.3 Rates and Slope Intercept Form Lesson Objectives 3.3 Rates and Slope-Intercept Form Press the tabs to view details. Standards

More information

HIGH-LOW METHOD. Key Terms and Concepts to Know

HIGH-LOW METHOD. Key Terms and Concepts to Know HIGH-LOW METHOD Key Terms and Concepts to Know Variable, Fixed and Mixed Costs Many costs are clearly variable, such as direct labor and direct materials, or clearly fixed, such as rent and salaries. Other

More information

Name: Class: Date: in general form.

Name: Class: Date: in general form. Write the equation in general form. Mathematical Applications for the Management Life and Social Sciences 11th Edition Harshbarger TEST BANK Full clear download at: https://testbankreal.com/download/mathematical-applications-management-life-socialsciences-11th-edition-harshbarger-test-bank/

More information

Using the Budget Features

Using the Budget Features Using the Budget Features 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 to determine

More information

Links to Maryland High School Mathematics Core Learning Goals

Links to Maryland High School Mathematics Core Learning Goals Title: Exploring Exponential Growth and Decay Functions Brief Overview: In this unit, students will use and apply exponential functions of growth and decay in realworld situations. Students will collect

More information

The Least Squares Regression Line

The Least Squares Regression Line The Least Squares Regression Line Section 5.3 Cathy Poliak, Ph.D. cathy@math.uh.edu Office hours: T Th 1:30 pm - 3:30 pm 620 PGH & 5:30 pm - 7:00 pm CASA Department of Mathematics University of Houston

More information

DATA HANDLING Five-Number Summary

DATA HANDLING Five-Number Summary DATA HANDLING Five-Number Summary The five-number summary consists of the minimum and maximum values, the median, and the upper and lower quartiles. The minimum and the maximum are the smallest and greatest

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

Seven Steps of Constructing Projects

Seven Steps of Constructing Projects I. Who are you? Seven Steps of Constructing Projects Agenda Assuming no responsibility, If you could immerse yourself for 4 hours doing something you love but never have 4 hours to do WHAT WOULD YOU DO?

More information

b. Find an expression for the machine s book value in the t-th year of use (0 < t < 15).

b. Find an expression for the machine s book value in the t-th year of use (0 < t < 15). Section 1.5: Linear Models An asset is an item owned that has value. Linear Depreciation refers to the amount of decrease in the book value of an asset. The purchase price, also known as original cost,

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

1. You are given two pairs of coordinates that have a linear relationship. The two pairs of coordinates are (x, y) = (30, 70) and (20, 50).

1. You are given two pairs of coordinates that have a linear relationship. The two pairs of coordinates are (x, y) = (30, 70) and (20, 50). Economics 102 Fall 2017 Answers to Homework #1 Due 9/26/2017 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework

More information

Test 1 Review MATH 176 Part 1: Computer Part

Test 1 Review MATH 176 Part 1: Computer Part / Test Review MATH 76 Part : Computer Part. Daniel buys a new car for $54,000. The car is epected to last 0 years, at which time it will be worth $7,000. a) Write a function that describes the value of

More information

Cosumnes River College Principles of Macroeconomics Problem Set 5 Due March 27, 2017

Cosumnes River College Principles of Macroeconomics Problem Set 5 Due March 27, 2017 Spring 2017 Cosumnes River College Principles of Macroeconomics Problem Set 5 Due March 27, 2017 Name: Prof. Dowell Instructions: Write the answers clearly and concisely on these sheets in the spaces provided.

More information

Math 166: Topics in Contemporary Mathematics II

Math 166: Topics in Contemporary Mathematics II Math 166: Topics in Contemporary Mathematics II Ruomeng Lan Texas A&M University October 15, 2014 Ruomeng Lan (TAMU) Math 166 October 15, 2014 1 / 12 Mean, Median and Mode Definition: 1. The average or

More information

ECO 2013: Macroeconomics Valencia Community College

ECO 2013: Macroeconomics Valencia Community College ECO 2013: Macroeconomics Valencia Community College Exam 3 Fall 2008 1. The most important determinant of consumer spending is: A. the level of household debt. B. consumer expectations. C. the stock of

More information

Economics 102 Discussion Handout Week 14 Spring Aggregate Supply and Demand: Summary

Economics 102 Discussion Handout Week 14 Spring Aggregate Supply and Demand: Summary Economics 102 Discussion Handout Week 14 Spring 2018 Aggregate Supply and Demand: Summary The Aggregate Demand Curve The aggregate demand curve (AD) shows the relationship between the aggregate price level

More information

Normal Probability Distributions

Normal Probability Distributions C H A P T E R Normal Probability Distributions 5 Section 5.2 Example 3 (pg. 248) Normal Probabilities Assume triglyceride levels of the population of the United States are normally distributed with a mean

More information

SA2 Unit 4 Investigating Exponentials in Context Classwork A. Double Your Money. 2. Let x be the number of assignments completed. Complete the table.

SA2 Unit 4 Investigating Exponentials in Context Classwork A. Double Your Money. 2. Let x be the number of assignments completed. Complete the table. Double Your Money Your math teacher believes that doing assignments consistently will improve your understanding and success in mathematics. At the beginning of the year, your parents tried to encourage

More information

Analyzing Accumulated Change: More Applications of Integrals & 7.1 Differences of Accumulated Changes

Analyzing Accumulated Change: More Applications of Integrals & 7.1 Differences of Accumulated Changes Chapter 7 Analyzing Accumulated Change: More Applications of Integrals & 7.1 Differences of Accumulated Changes This chapter helps you effectively use your calculatorõs numerical integrator with various

More information

Consider the aggregate production function for Dane County:

Consider the aggregate production function for Dane County: Economics 0 Spring 08 Homework #4 Due 4/5/7 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly).

More information

L K Y Marginal Product of Labor (MPl) Labor Productivity (Y/L)

L K Y Marginal Product of Labor (MPl) Labor Productivity (Y/L) Economics 102 Summer 2017 Answers to Homework #4 Due 6/19/17 Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework

More information

SPIRIT 2.0 Lesson: Am I Straight?

SPIRIT 2.0 Lesson: Am I Straight? SPIRIT 2.0 Lesson: Am I Straight? ===============================Lesson Header ============================== Lesson Title: Am I Straight? Draft Date: July 21, 2008 1st Author (Writer): Neil Hammond 2nd

More information

Petrochemical Production p (Billions of metric tons)

Petrochemical Production p (Billions of metric tons) Off-Line Homework Section 1.1 WebAssign Section 1.1 #13 (ebook 1.1#42) The following table shows the annual petrochemical production p in Mexico by Pemex, Mexico s national oil company, for 2005-2010 (t

More information

When changing any conditions of an investment or loan, the amount or principal will also change.

When changing any conditions of an investment or loan, the amount or principal will also change. KEY CONCEPTS When changing any conditions of an investment or loan, the amount or principal will also change. Doubling an interest rate or term more than doubles the total interest This is due to the effects

More information

MLC at Boise State Logarithms Activity 6 Week #8

MLC at Boise State Logarithms Activity 6 Week #8 Logarithms Activity 6 Week #8 In this week s activity, you will continue to look at the relationship between logarithmic functions, exponential functions and rates of return. Today you will use investing

More information

SJAM MPM 1D Unit 5 Day 13

SJAM MPM 1D Unit 5 Day 13 Homework 1. Identify the dependent variable. a) The distance a person walks depends on the time they walk. b) The recipe for 1 muffins requires cups of flour. c) Houses need 1 fire alarm per floor.. Identify

More information

WEEK 1 REVIEW Lines and Linear Models. A VERTICAL line has NO SLOPE. All other lines have change in y rise y2-

WEEK 1 REVIEW Lines and Linear Models. A VERTICAL line has NO SLOPE. All other lines have change in y rise y2- WEEK 1 REVIEW Lines and Linear Models SLOPE A VERTICAL line has NO SLOPE. All other lines have change in y rise y- y1 slope = m = = = change in x run x - x 1 Find the slope of the line passing through

More information

Name: Date: 1. Which graph correctly shows the slope? 1 A. B. C. D. 2. Look at the table below

Name: Date: 1. Which graph correctly shows the slope? 1 A. B. C. D. 2. Look at the table below Name: Date: 1. Which graph correctly shows the slope? 1 2. Look at the table below. -4-28 -1-10 3 14 8 44 12 68 Which equation represents the relationship of to? Office of Academics and Transformation

More information

Week 19 Algebra 2 Assignment:

Week 19 Algebra 2 Assignment: Week 9 Algebra Assignment: Day : pp. 66-67 #- odd, omit #, 7 Day : pp. 66-67 #- even, omit #8 Day : pp. 7-7 #- odd Day 4: pp. 7-7 #-4 even Day : pp. 77-79 #- odd, 7 Notes on Assignment: Pages 66-67: General

More information

False_ The average revenue of a firm can be increasing in the firm s output.

False_ The average revenue of a firm can be increasing in the firm s output. LECTURE 12: SPECIAL COST FUNCTIONS AND PROFIT MAXIMIZATION ANSWERS AND SOLUTIONS True/False Questions False_ If the isoquants of a production function exhibit diminishing MRTS, then the input choice that

More information

5.5: LINEAR AUTOMOBILE DEPRECIATION OBJECTIVES

5.5: LINEAR AUTOMOBILE DEPRECIATION OBJECTIVES Section 5.5: LINEAR AUTOMOBILE DEPRECIATION OBJECTIVES Write, interpret, and graph a straight line depreciation equation. Interpret the graph of a straight line depreciation. Key Terms depreciate appreciate

More information

Perfect Competition. Profit-Maximizing Level of Output. Profit-Maximizing Level of Output. Profit-Maximizing Level of Output.

Perfect Competition. Profit-Maximizing Level of Output. Profit-Maximizing Level of Output. Profit-Maximizing Level of Output. erfect Competition Chapter 14-2. rofit Maximizing and Shutting Down rofit-maximizing Level of The goal of the firm is to maximize profits. rofit is the difference between total revenue and total cost.

More information

Lesson-36. Profit Maximization and A Perfectly Competitive Firm

Lesson-36. Profit Maximization and A Perfectly Competitive Firm Lesson-36 Profit Maximization and A Perfectly Competitive Firm A firm s behavior comes within the context of perfect competition. Then comes the stepby-step explanation of how perfectly competitive firms

More information

STATISTICAL DISTRIBUTIONS AND THE CALCULATOR

STATISTICAL DISTRIBUTIONS AND THE CALCULATOR STATISTICAL DISTRIBUTIONS AND THE CALCULATOR 1. Basic data sets a. Measures of Center - Mean ( ): average of all values. Characteristic: non-resistant is affected by skew and outliers. - Median: Either

More information

Name Student ID # Instructor Lab Period Date Due. Lab 6 The Tangent

Name Student ID # Instructor Lab Period Date Due. Lab 6 The Tangent Name Student ID # Instructor Lab Period Date Due Lab 6 The Tangent Objectives 1. To visualize the concept of the tangent. 2. To define the slope of the tangent line. 3. To develop a definition of the tangent

More information

Cost-Volume-Profit Analysis

Cost-Volume-Profit Analysis Cost-Volume-Profit Analysis Chapter 21 PowerPoint Editor: Beth Kane, MBA, CPA Wild, Shaw, and Chiappetta Fundamental Accounting Principles 22nd Edition Copyright 2015 McGraw-Hill Education. All rights

More information

Week 7. Texas A& M University. Department of Mathematics Texas A& M University, College Station Section 3.2, 3.3 and 3.4

Week 7. Texas A& M University. Department of Mathematics Texas A& M University, College Station Section 3.2, 3.3 and 3.4 Week 7 Oğuz Gezmiş Texas A& M University Department of Mathematics Texas A& M University, College Station Section 3.2, 3.3 and 3.4 Oğuz Gezmiş (TAMU) Topics in Contemporary Mathematics II Week7 1 / 19

More information

Section 7C Finding the Equation of a Line

Section 7C Finding the Equation of a Line Section 7C Finding the Equation of a Line When we discover a linear relationship between two variables, we often try to discover a formula that relates the two variables and allows us to use one variable

More information

σ e, which will be large when prediction errors are Linear regression model

σ e, which will be large when prediction errors are Linear regression model Linear regression model we assume that two quantitative variables, x and y, are linearly related; that is, the population of (x, y) pairs are related by an ideal population regression line y = α + βx +

More information

Chapter 4. Determination of Income and Employment 4.1 AGGREGATE DEMAND AND ITS COMPONENTS

Chapter 4. Determination of Income and Employment 4.1 AGGREGATE DEMAND AND ITS COMPONENTS Determination of Income and Employment Chapter 4 We have so far talked about the national income, price level, rate of interest etc. in an ad hoc manner without investigating the forces that govern their

More information