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Ch. 8 Sections 1 – 6 Practice Test Name _________________________ Period _____________ 1. Determine whether each function represents exponential growth or decay. What is the growth/decay factor? Find the percent of increase or decrease that the function models. a) y 61.4 x b) y 0.20.72 1 c) y 2.7 5 x x 2. Graph the functions. a) y 3(2) 1 b) y 3 2 x x c) y 2 x3 4 4. Suppose you invest $6,800 at an annual interest rate of 5.2% compounded continuously. Find the amount you will have in the account after 13 years. x 8 3 5. Given the function y 0.14 4 . Is the function a stretch, shrink, or neither, and is the e function exponential growth or exponential decay. Circle the correct words. 6. Pythag-2 is used to locate brain problems. It has a half-life of 48 days. Write an exponential decay function for a 80-mg sample. Use the function to find the amount remaining after 100 days. 7. Solve. Round your answers to three decimal places. a) 6 x 40 b) 50 2(5) x4 c) 32 2 x 3 8 6 x 8 d) 7 x 3 89 f) 2 6 x 3 17 44 e) 114 x 1 56 8. Write in logarithmic form. a) 9 4 6561 b) 2 4 1 16 9. Write in exponential form. a) log 4 4096 6 1 b) log 2 3 8 10. Evaluate each logarithm. a) log 4 32 b) log 9 243 11. Graph the functions. a) y log 3 x b) y log 3 x 2 12. Write each logarithmic expression as a single logarithm. 2 a) log 16 log 10 log 3 b) 10 log y 5 log m log n 3 d) 3 log M log P 4 log X c) 1 2 log 144 log 2 log 8 3 3 e) 9 ln x 5 ln 5 8 ln m 4 ln y 13. Expand each logarithm. a) log 7 x 4 y b) log c2d 4 e w6 3 P c) log K 14. If log 2 5 x and log 2 3 y , rewrite the expression in terms of x and/or y. 3 a) log 2 15 b) log 2 c) log 2 0.45 5 15. Solve. Round your answers to three decimal places. a) log 17 x 1 2 b) log 2 8 log 2 5x 2 4 d) log (5 x 12) 3 e) ln 3x 6 c) log 4 8x log 4 x 3 f) ln 3 x 2 5 2 g) ln x 1 3 2 x7 h) ln 2 5 i) 2 ln 5x ln 6 3 16. Solve. Round your answers to three decimal places. a) e x2 11 b) e 5 x 1 21 c) e x 6 18 52 17. An initial deposit of $6300 is now worth $8073.20. The account earns 3.1% interest and is compounded continuously. For how long has the money been in the account? 18. If the parent function of an exponential function is f ( x) 6 x , write the equation for this function if it were stretched by a factor of 3, translated 4 units to the right, and 11 units up. 19. What are two real-world applications of logarithms?