Unit 7 Exponential and Logarithms Review Problems Algebra

Unit 7 Exponential and Logarithms Review Problems Algebra 2 7 -R

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x=2 26 Review Problems

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x=15 30 Review Problems

x=64 31 Review Problems

q=1 y=14 32 Review Problems

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x=5 38 Review Problems

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y=-2. 6977 42 Review Problems

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x=2. 1972 44 Review Problems

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• For Dave to buy a new car comparably equipped to the one he bought years ago would cost $12, 500. Since Dave bought the car, the inflation rate for cars like his has been at an average annual rate of 5. 1%. If Dave originally paid $8400 for the car, how long ago did he buy it? 49 Review Problems

• Cobalt, an element used to make alloys, has several isotopes. One of these, cobalt-60, is radioactive and has a half-life of 5. 7 years. Cobalt-60 is used to trace the path of nonradioactive substances in a system. What is the value of k for Cobalt-60? 50 Review Problems

• Modern whales appeared 510 million years ago. The vertebrae of a whale discovered by paleontologists contain roughly 0. 25% as much carbon-14 as they would have contained when the whale was alive. How long ago did the whale die? Use k=0. 00012 51 Review Problems

• The population of rabbits in an area is modeled by the growth equation P(t) 8 e 0. 26 t, where P is in thousands and t is in years. How long will it take for the population to reach 25, 000? 52 Review Problems

• How many hours will it take a culture of bacteria to increase from 20 to 2000 if the growth rate per hour is 85%? 53 Review Problems

• A radioactive substance has a half-life of 32 years. Find the constant k in the decay formula for the substance. 54 Review Problems

• A piece of machinery valued at $250, 000 depreciates at a fixed rate of 12% per year. After how many years will the value have depreciated to $100, 000? 55 Review Problems

• In an over-fished area, the catch of a certain fish is decreasing at an average rate of 8% per year. If this decline persists, how long will it take for the catch to reach half of the amount before the decline? 56 Review Problems

• Alex invests $2000 in an account that has a 6% annual rate of growth. To the nearest year, when will the investment be worth $3600? 57 Review Problems

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1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. ANSWERS

21. 22. 23. 24. 25. 26. x=2 27. 28. 29. 30. x=15 31. 32. q=1 33. 34. 35. 36. 37. 38. x=5 39. 40. ANSWERS x=64 y=14

41. 42. y=-2. 6977 43. 44. x=2. 1972 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. ANSWERS