Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algebra 2 Chapter 7 Review: Exponential & Logarithmic Functions Name: Tell whether the function represents exponential growth or exponential decay. 1. 2. 1 5 f x 2 7 x 1 7 f x 3 5 3. x f x 3 4 x 4. 5. 6. 1 f x e5x 5 1 f x e x 2 f x 2e3x Explain how the graph of g can be obtained from the graph of f. f x 3x f x 10 x 7. 8. g x 3x 5 4 g x 10 x 2 Simplify the expression. 9. 10 x 10. 64e e e x 1 e 4e 2 11. 5 e e7 12. 3e4 2 Graph the function. Give the asymptote, domain, and range. 13. f x 3 x 2 1 3 14. f x 5 x 1 3 15. f x 1 log2 x 2 Asymptote: Asymptote: Asymptote: Domain: Domain: Domain: Range: Range: Range: 1 17. f x e2 x 1 2 16. f x ln x 1 18. f x e3x 1 Asymptote: Asymptote: Asymptote: Domain: Domain: Domain: Range: Range: Range: Rewrite the equation in exponential form. 1 19. log 5 1 5 Rewrite the equation in logarithmic form 21. 73 343 Evaluate the logarithm without using a calculator. 1 23. log8 2 24. log 2 4 Find the inverse of the function. 27. f x log x 1 28. f x 3 log6 x 20. ln1 0 22. r t w 25. log 1 125 5 29. f x 5 ln x 3 Use the change of base formula and your calculator to evaluate the following. 31. log8 2000 32. log 1 5 33. log e 125 3 26. ln e5 30. y 4e x 1 3 Expand the expression. x2y 34. log2 5z Condense the expression. 2 36. log2 x 3log2 y 3 35. log 37. 1 log 4 x log 4 z 3 10 7 x 38. log3 4 2log3 x log3 5 log3 w Solve the equation. Round the result to three decimal places if necessary. 3 39. 23 x 1 10 40. 3e x 4 13 41. 95 x 272 x 1 8 42. ln 5x 1 ln 3x 2 45. log4 x log4 x 3 1 43. 9log3 x 4 11 44. 8 2 log2 3x 46. log x log3 2 47. You invest $900 in an account that pays 4.5% annual interest. How much will you have in 12 years if it is compounded daily? Continuously? 48. You deposit $2000 into an account that pays 2% annual interest compounded quarterly. How long will it take for the balance to reach $2500? 49. You buy a new car for $22,000. The value of the car decreases by 12.5% each year. Write an exponential model for the value V of the car after t years. What is the value of the car after 3 years? When will the value of the car be $8,000? 50. You have inherited land that was purchased for $30,000 in 1960. The value V of the land increased by approximately 5% per year. Write a model for the value of the land t years after 1960. What is the approximate value of the land in the year 2010? Use your calculator to find an exponential model for the data. 51. x 1 2 3 4 5 y 3.6 8.64 20.736 49.766 119.439 6 286.654 7 687.971 Use the properties of logarithms to rewrite the expression in terms of log 3 and log 4. Then use log 3 and log 4 to approximate the expression. DO NOT USE A CALCULATOR!!! 4 52. log12 53. log 54. log16 27 8 1651.13