Go for the Curve! Comparing Linear and Exponential Functions. Lesson 5.1 Assignment

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1 Lesson.1 Assignment Name Date Go for the Curve! Comparing Linear and Exponential Functions 1. Chanise just received a $200 bonus check from her employer. She is going to put it into an account that will earn interest. The Basic savings account at her bank earns 6% simple interest. The Gold savings account earns 4.% compound interest. a. Write a function for each account that can be used to determine the balance in the account based on the year, t. Describe each function. b. Use your answers to part (a) to complete the table. Round the values to the nearest cent. Quantity Time Basic Savings Account Balance Gold Savings Account Balance Units Expression Chapter Assignments 61

2 Lesson.1 Assignment page 2 c. Graph the functions for the Basic and Gold Savings accounts on your graphing calculator. Then, sketch the graphs below. d. Into which account would you recommend that Chanise deposit her money? Explain your reasoning. e. After reading the pamphlet about the different accounts a little more closely, Chanise realizes that there is a one-time fee of $300 for depositing her money in the Gold account. Does this change the recommendation you made in part (d)? Why or why not? f. Compare the rates of change for the Basic and Gold savings accounts. Explain what the rates of change tell you about the accounts. g. What do the rates of change for linear and exponential functions tell you about the graphs of the functions? 62 Chapter Assignments

3 Lesson.2 Assignment Name Date Downtown and Uptown Graphs of Exponential Functions 1. Tyler recently purchased a new car for $,000. He also purchased a vintage older car for $30,000. The new car will start depreciating the minute he drives it off the lot and will decrease in value by 10% each year. Because the older car is a collector s item, it will increase in value by % each year. a. Complete the table to show the values of the cars after t years. Time (years) t Value of New Car (dollars) Value of Vintage Car (dollars) b. Determine the rates of increase and decrease for the functions between and 20 years. Are the rates increasing or decreasing at a constant rate? Why or why not? c. What is the common ratio in simplest form for the sequence each function represents? Chapter Assignments 63

4 Lesson.2 Assignment page 2 d. Graph both functions using a graphing calculator. Determine the y-intercepts of the functions. Explain what they mean in terms of the problem situation. e. Determine how long it will take the new car to depreciate to half of its original value. Explain your method. f. How many years from now will the value of the cars be the same? Determine the approximate values. g. What is the domain and range for each of the functions? What do the domain and range need to be in order to make sense of the problem? h. What is the equation for the asymptote of the value functions for each car? How does this relate to the problem? 64 Chapter Assignments

5 Lesson.3 Assignment Name Date Let the Transformations Begin! Translations of Linear and Exponential Functions Bryon is raising money for a surfing trip by selling coupon books. He earns $10 toward his trip for every book he sells. 1. Analyze the problem situation. a. Complete the table to determine the amount of money Bryon will earn after selling x coupon books. Number of Coupon Books x Amount of Money b. Before Bryon is able to begin selling the coupon books, the company selling the books goes under new management. In order to try to make more profit, management informs Bryon that they will give him $10 for every book he sells over books. Complete the table to determine how much money Bryon will earn after selling x coupon books. Number of Coupon Books Amount of Money Chapter Assignments 6

6 Lesson.3 Assignment page 2 c. Graph both situations. Label the graphs. y Amount of Money (dollars) Number of Coupon Books x d. Compare the graphs. Then write the function for the amount of money earned under new management g(x) in terms of the basic function f(x). 2. Bryon was able to raise $40 selling coupon books. He decided to put his money into a savings account that earns 3% annual compound interest. a. Write the function that represents the amount of money Bryon will have after x years. Use f(x) for the function. b. Complete the table to determine how much money Bryon will have after x years. Number of Years Amount of Money 66 Chapter Assignments

7 Lesson.3 Assignment page 3 Name Date c. Bryon s father is extremely proud of Byron s decision to put the money into a savings account. He tells him that he will give him an additional $300 at the time he takes the money out of savings. Complete the table for the amount of money Bryon will have after saving the money for x years. Number of Years Amount of Money d. Graph both situations. Label the graphs. y Amount of Money (dollars) Number of Years x e. Compare the graphs. Then, write the function for the amount of money earned after Bryon s father contributes g(x) in terms of the basic function f(x). Chapter Assignments 67

8 68 Chapter Assignments

9 Lesson.4 Assignment Name Date Take Some Time to Reflect Reflections of Linear and Exponential Functions 1. The Haverston Daily News had 20,000 subscribers in 200. They determined that over the past years the number of subscribers decreased steadily by 10% each year. a. Determine the function, f(x), for the number of subscribers based on x, the number of years past 200. b. Write the equation of a function g(x) that is a reflection of f(x) about the horizontal line y 0. Then write the equation of a function h(x) that is a reflection of f(x) about the vertical line x 0. c. Without graphing, describe how the graphs of g(x) and h(x) will compare to the graph of their basic function f(x). Explain your reasoning. d. Use a graphing calculator to graph the functions f(x), g(x), and h(x). Then sketch and label the graph of each function. Chapter Assignments 69

10 Lesson.4 Assignment page 2 2. The city of Springfield has determined that their newspaper subscribers have declined at a steady rate of about 320 readers each year since 200 when they had 24,000 subscribers. a. Determine the linear function, m(x), for the number of subscribers based on x, the number of years past 200. b. The function m(x) has been transformed three different ways. The results are n(x), p(x), and r(x). Describe how m(x) was transformed to produce the other functions. Then, write an equation for each of those functions. m(x) y r(x) 32,000 24,000 16, , n(x) 28, , , x p(x) 232, Chapter Assignments

11 Lesson. Assignment Name Date Radical! Because It s Cliché! Properties of Rational Exponents 1. Use the formulas in the table to answer the questions. Name of Formula Formula Definition of Variables Volume of a sphere Period of a pendulum Wingspan of a bird V 4 3 pr3 r radius T < 2p L g L length of pendulum g acceleration due to gravity L 2.43 w w weight of bird a. Determine the radius of a sphere with a volume of cubic units. Use 3.14 for p. Show your work. b. Trevor and Yasmine have rewritten the formula for the period of a pendulum using rational exponents. Their answers are shown below. Determine which student rewrote the formula correctly, and explain the mistake the other student made. Trevor: T < 2p ( L g ) 1 2 Yasmine: T < 2p ( L g ) Chapter Assignments 71

12 Lesson. Assignment page 2 c. Rewrite the formula for the length of the wingspan of a bird using radicals and exponents. Explain how you determined your answer. 2. Mr. Ashman writes the expression ( 8 27 ) 23 on the board and asks his students to simplify the expression completely. The work of three students is shown below. Analyze each student s work and determine who simplified the expression correctly. Explain the mistakes the other students made. Student 1 Student 2 Student 3 ( 8 27 ) 23 1 ( 8 27 ) 3 ( 8 27 ) 23 1 ( ) 3 ( 8 27 ) 23 1 ( 8 27 ) 3 1 ( ) , , Chapter Assignments

13 Lesson.6 Assignment Name Date Checkmate! Solving Exponential Functions Roberto and Maeko open a pet store. They sell fish, birds, and small mammals. 1. Roberto and Maeko start with hamsters for sale. Hamster populations usually triple every cycle. One cycle is equal to 4 months. Determine the number of hamsters they will have after each cycle. Cycle Number of Hamsters a. Graph the points from your table. y x Chapter Assignments 73

14 Lesson.6 Assignment page 2 b. Does it make sense to connect the points in this graph? Why or why not? c. Write an equation in function notation to represent the change in the number of hamsters as a function of the cycle number, c. Explain how you determined your equation. d. Determine the cycle at which there will be 32,80 hamsters. In how many months will this be? Explain how you determined your answer. e. After how many cycles will there be at least 98,000 hamsters? In how many months will this be? Explain how you determined your answer. f. Robert and Maeko are overwhelmed by hamsters. They counted the hamsters and now have 10,93 of them. What cycle has just completed? Show your work. 74 Chapter Assignments

15 Lesson.6 Assignment page 3 Name Date 2. Robert and Maeko have 20 large tanks of fish in their store. They notice that one of the larger tanks is losing water, but they can t find the leak. The tank started with 40 gallons of water, but appears to be leaking two-thirds of its water each hour. This means that after the first hour the tank has one-third of the water left, or 10 gallons. Complete the table to show the amount of water the tank will have after each hour. Write each amount as a whole number, mixed number, or fraction. Hour Amount of Water (gallons) a. Graph the points from your table. y x Chapter Assignments 7

16 Lesson.6 Assignment page 4 b. Does it make sense to connect the points in this graph? Why or why not? c. Write an equation in function notation to represent the gallons of water in the tank after any hour, t. Write the function in two ways: one with a positive exponent and the other with a negative exponent. Explain how you determined your answers. 76 Chapter Assignments

3.1 Exponential Functions and Their Graphs Date: Exponential Function

3.1 Exponential Functions and Their Graphs Date: Exponential Function Exponential Function: A function of the form f(x) = b x, where the b is a positive constant other than, and the exponent, x, is a variable.