Small Investment, Big Reward

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1 Lesson.1 Assignment Name Date Small Investment, Big Reward Exponential Functions 1. Wildlife biologists are studying the coyote populations on 2 wildlife preserves to better understand the role climate plays in population change. The table displays the coyote populations on both preserves for each year of the study. The Year 0 corresponds to the date of the biologists initial observations at the start of their study. Year Alaska Preserve Tennessee Preserve a. Do the populations represent arithmetic or geometric sequences? Explain your reasoning. b. For each wildlife preserve, write a sequence to represent the coyote population in a given year. c. For each wildlife preserve, write a function to represent the coyote population as a function of the year of the study. Chapter Assignments 139

2 Lesson.1 Assignment page 2 d. Use the functions you wrote in part (c) to complete the table. Round all answers to the nearest whole number. e. Graph and label the functions you wrote in part (c). 900 y Coyote Population x Year of Study f. Do the populations represent examples of exponential decay, exponential growth, or neither? Explain your reasoning. g. Will the coyote population on the Tennessee preserve ever exceed the coyote population on the Alaska preserve? If so, when will this occur? h. Make a hypothesis about the role the climate plays on coyote populations based on the results of the study, assuming all other population growth factors are equal. Explain your reasoning. 140 Chapter Assignments

3 Lesson.2 Assignment Name Date We Have Liftoff! Properties of Exponential Graphs 1. Caleb wants to invest $00 in a savings account. Lincoln Federal Bank is offering 6% interest compounded yearly. Washington National Bank is offering 5.5% interest compounded daily. a. For each bank, write an exponential function to represent the amount of money Caleb would have in the account after t years. b. Determine which bank Caleb should choose if he plans to invest his money for 5 years. If Caleb decides to leave the money in the bank for a longer period of time, will the other bank be a better deal in the long run? Explain your reasoning. c. Complete the table for the 2 functions you wrote in part (a). Summarize the characteristics in terms of the problem situation. Domain Range Lincoln Federal Bank Washington National Bank Intercepts Right End Behavior Intervals of Increase or Decrease Chapter Assignments 141

4 Lesson.2 Assignment page 2 2. In 20, Bolivia had a population of.5 million people and an annual growth rate of 1.6%. a. Write a function to model Bolivia s population with respect to t, the number of years since 20. Write your function in the form N(t) 5 N 0 e rt. b. Use your model to predict what Bolivia s population will be in the year c. Use your model to estimate Bolivia s population in the years 1990 and d. Use a graphing calculator to estimate when Bolivia s population will reach 20 million people. 142 Chapter Assignments

5 Lesson.2 Assignment page 3 Name Date e. Discuss the domain, range, asymptotes, intercepts, end behavior, and intervals of increase and decrease for your population model as they relate to the problem situation. Chapter Assignments 143

6 144 Chapter Assignments

7 Lesson.3 Assignment Name Date I Like to Move It Transformations of Exponential Functions 1. Given: f(x) 5 2 x and g(x) 5 f ( 1 3 x ). The graph of f(x) is shown. y 8 f(x) x a. Complete the y-values for each of the reference points on f(x) in the table. Reference Points on f(x) ( 21, ) Corresponding Points on g(x) (0, ) (1, ) b. Complete the table in part (a) to determine the points on g(x) that correspond to each of the reference points on f(x). c. Sketch and label the graph of g(x) on the coordinate plane. Chapter Assignments 145

8 Lesson.3 Assignment page 2 d. Describe the transformation on the graph of f(x) that produces g(x). e. Write g(x) as an exponential function. f. Describe the effect the transformation had on the domain, range, asymptotes, intercepts, end behaviors, and intervals of increase and decrease. Explain your reasoning. 2. Given: p(x) 5 5 x and t(x) 5 p(2x) 2 4. a. Describe the transformation on the graph of p(x) that produces t(x). b. Write t(x) as an exponential function. 3. Given: m(x) x and k(x) m(2x). a. Describe the transformation on the graph of m(x) that produces k(x). b. Write k(x) as an exponential function. 146 Chapter Assignments

9 Lesson.4 Assignment Name Date I Feel the Earth Move Logarithmic Functions 1. Given: f(x) 5 3 x. a. Write the function f 21 (x), the inverse of f(x) 5 3 x. b. Graph and label the functions f(x) and f 21 (x) on the coordinate plane. 8 y x c. Describe how to calculate f 21 (3) without a calculator. Then, calculate f 21 (3), f 21 (9), and f 21 (27). d. Determine the domain, range, asymptotes, intercepts, end behavior, and intervals of increase and decrease for f 21 (x). Chapter Assignments 147

10 Lesson.4 Assignment page 2 2. The loudness of sounds is measured in decibels (db). The loudness, L, of a sound is a function of its intensity, I, and can be determined using the function L(I ) 5 log ( I I 0 ), where both I and I 0 are measured in watts per square meter (W/ m 2 ). In the function, I 0 represents a barely audible sound or threshold sound and is equal to 212 W/ m 2. a. The Guinness World Record for the Loudest Crowd Roar at an Outdoor Stadium was set during an NFL game in Seattle. The roar measured db. During an NFL game in Kansas City, the roar of the crowd was measured at db. How many times more intense was the roar at the Seattle game? b. The fans in Kansas City attempted to break the Guinness World Record for the Loudest Crowd Roar. Their goal was to create a roar that was 2 times as intense as the Seattle roar. In order for the fans in Kansas City to be successful, how many decibels did their roar need to be? c. In fact, the fans in Kansas City successfully recorded a new record of 140 db. Determine the intensity of the roar. 148 Chapter Assignments

11 Lesson.5 Assignment Name Date More Than Meets the Eye Transformations of Logarithmic Functions 1. Consider the function g(x), which is formed by translating the function f(x) 5 log 2 x left 3 units and up 4 units. a. Write g(x) in terms of f(x). b. Complete the table by determining the corresponding point on g(x) for each reference point on f(x). Reference Point on f(x) Corresponding Point on g(x) (0.5, 21) (1, 0) (2, 1) (4, 2) c. Graph and label g(x). 8 y 6 4 f(x) x d. Write g(x) as a logarithmic function. e. List the domain, range, and any asymptotes of the logarithmic function g(x). Chapter Assignments 149

12 Lesson.5 Assignment page 2 2. Consider p(x) 5 2 x 3, which is a transformation of the function f(x) 5 2 x. a. Describe the transformation(s) on the graph of f(x) to produce p(x). b. Write the equations of the inverse functions f 21 (x) and p 21 (x). c. Describe the transformation(s) on the graph of f 21 (x) to produce p 21 (x). d. Graph and label the inverse function p 21 (x). 8 y x Chapter Assignments

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