Assignment. Growth, Decay, and Interest Exponential Models. Write an exponential function to model each situation.

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1 Assignment Assignment for Lesson.1 Name Date Growth, Decay, and Interest Exponential Models Write an exponential function to model each situation. 1. A town s population was 78,400 in 10. The population has been decreasing at a rate of 2.5% each year. Write an equation that models the town s population P, where t represents the number of years after Melissa deposits $650 into an account that earns 4.2% interest compounded monthly. Write an equation that represents the balance P in Melissa s account after t years. 3. A radioactive element has a half-life of 240 years. There are 750 grams of the element. Write a formula for the amount of radioactive material left, N, after t years. 4. In a computer lab, 2 computers are infected with a virus. Each hour, the newly infected computers infect 5 other computers with the virus. Write a function that models the number of computers S that are affected each hour after t hours. A scientist is studying a colony of insects. The insect population increases at a rate of about 23% per month. The scientist began his study with 16 insects. 5. Write a function that models the insect population P where t represents the time in months. Chapter Assignments 165

2 6. What was the insect population after 2 months? 7. What was the insect population after 2 years? 8. Graph the function on the following grid.. When will the insect population reach 1000? 10. When will the insect population reach 2000? 166 Chapter Assignments

3 Assignment Assignment for Lesson.2 Name Date Too Much Homework! Geometric Sequences, Series, and Partial Sums Write the first six terms of the geometric sequence with each given set of criteria. 1. The first term of the sequence is 3 and the common ratio is The first term of the sequence is 128 and the common ratio is Write a recursive formula and an explicit formula that represent the nth term of each geometric sequence. 3. 7, 14, 28, 56, , 8, 32, 128, , 15, 45, 135, , 150, 225, Calculate the specified sum of each geometric sequence , 243, 81, 27,... ; S , 2, 4, 8,... ; S 18 Chapter Assignments 167

4 5. 10, 5,,... ; S , 0.8, 3.2, 12.8,... ; S 2, 5 4, You propose a new plan for your allowance for next year. You ask that your parents give you 1 penny after the first week of the year, and then triple your allowance every week for the remainder of the year. a. Write a formula that you can use to find the total allowance you will have received after the nth week of the year under the new plan. b. What is the total allowance you will have received after the 10th week of the year? c. What is the total allowance you will have received after the 20th week of the year? d. Do you think that your parents will agree with your proposal? Why or why not? 168 Chapter Assignments

5 Assignment Assignment for Lesson.3 Name Date Sequences, Series, and Exponentials Geometric Sequences and Series as Exponential Functions Write each geometric sequence as an exponential function. 1. 1, 6, 36, 216, , 50, 25, 12.5, g 1 384, g n g n 1 4. h 1 5, g n.4g n 1 Chapter Assignments 16

6 Graph each exponential function on the grid provided. Then write the exponential function as a geometric sequence and graph the sequence on the same grid. 5. f (x) 8 x 1 6. g(x) 0.8 x 1 7. c(x) 3(4) x 1 8. h(x) 2(0.3) x Chapter Assignments

7 Name Date For each given geometric sequence, rewrite the partial sums as an exponential function. Then graph the first five partial sums and the exponential function on the same grid.. 84, 42, 21, 10.5, h 1 11, g n g n 1 Chapter Assignments 171

8 172 Chapter Assignments

9 Assignment Assignment for Lesson.4 Name Date People, Tea, and Carbon Dioxide Modeling Using Exponential Functions Use your graphing calculator to find the exponential regression equation for each data set. Then graph the data points and the equation with the given window on your calculator and explain whether the equation fits the data well. 1. (0.5, 2), (0, 1), (1.5, 1.5), (1, 0.5), (2, 2), (0.5, 0.5), (2, 2.5), ( 1, 3.5) Window: 2 x 4, 0 y 4 2. (31, 22), ( 10, 41), ( 35, 8), (54, 15), (22, 20), (41, 18), (0, 28) Window: 40 x 60, 0 y 100 The following data shows the number of U.S. Post Offices at the beginning of each decade from 100 to Use this information to answer Questions 3 through 6. Year Number of U.S. Post Offices , , , , , , , , , , ,876 Chapter Assignments 173

10 3. Sketch a scatter plot of the data on the following grid. Let x 0 represent the year 100, x 10 represent the year 110, and so on. 4. Use your graphing calculator to find the exponential regression equation for the data set. Then graph the equation on the grid in Question Use the exponential regression equation to predict the number of U.S. Post Offices in the year Use the graph of the exponential regression equation to predict when the number of U.S. Post Offices will reach 20, Chapter Assignments

Geometric Sequences. Today I am: folding paper and counting the number of rectangles formed. So that I can: see how a geometric sequence is formed.

Geometric Sequences. Today I am: folding paper and counting the number of rectangles formed. So that I can: see how a geometric sequence is formed. LESSON 9 Geometric Sequences LEARNING OBJECTIVES Today I am: folding paper and counting the number of rectangles formed. So that I can: see how a geometric sequence is formed. I ll know I have it when