Algebra II



Algebra II Name: _______________________________________

Chapter 7 Review Period: _____________ Date: _____________________

Spring 2014

Part I – No calculator allowed

Please show all work where appropriate to receive full credit. Be aware that there will be two parts to the Chapter 7 Test – Part I – No calculator allowed and Part II – Calculator allowed. Do this review as if it were your test – use your calculator only on Part II.

Explain why it is a growth or decay problem.

1. [pic]

2. [pic]

3. [pic]

Write each equation in logarithmic form.

4. [pic]

5. [pic]

6. [pic]

Draw the parent graph with a dotted curve and the translation with a solid curve. State the domain, range, and asymptotes for the translated graphs.

7. [pic]

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8. [pic]

| |[pic] |

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|Domain: | |

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9. [pic]

| |[pic] |

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|Domain: | |

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Write each equation in exponential form.

10. [pic]

11. [pic]

12. [pic]

Evaluate each logarithm.

13. [pic] 14. [pic]

15. [pic] 16. [pic]

Draw the parent graph with a dotted curve and the translation with a solid curve. State the domain, range, and asymptotes for the translated graphs.

18. [pic]

| |[pic] |

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19. [pic]

| |[pic] |

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|Domain: | |

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19. [pic]

| |[pic] |

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|Domain: | |

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Solve the equation or inequality.

20. [pic]

21. [pic]

22. [pic]

Part II-Calculator Allowed

Use [pic] and [pic] to approximate the value of each expression.

23. [pic]

24. [pic]

25. [pic]

26. [pic]

Solve each equation. Give exact answers.

27. [pic]

28. [pic]

29. [pic]

Solve each equation. Give exact answers and then round to the nearest hundredth. Check for extraneous solutions.

30. [pic]

31. [pic][Condense logs on to one log first]

32. [pic] [Move logs to one side and condense as one log first]

Solve each equation or inequality. Give exact answers and then round to the nearest hundredth if applicable. Check for extraneous solutions.

33. [pic]

34. [pic]

35. [pic]

36. [pic]

37. [pic]

38. [pic]

39. [pic]

40. [pic]

41. [pic]

42. [pic]

43. [pic]

44. An initial investment of $350 is worth $429.20 after six years of continuous compounding. Find the interest rate.

45. A bacteria population started with 5000 bacteria. After 8 hours, there were 28,000 in the sample.

a. Write an exponential function that could be used to model the number of bacteria after x hours if the number of bacteria changes at the same rate.

b. How many bacteria can be expected in the sample after 32 hours?

46. The magnitude of an earthquake is measured on a logarithmic scale called the Richter scale. The magnitude M is given by [pic], where x represents the amplitude of the seismic wave causing ground motion. How many times as great is the amplitude caused by an earthquake with a Richter scale rating of 10 as an aftershock with a Richter scale rating of 7?

47. Use the formula [pic], where L is the loudness of a sound and R is the sound’s relative intensity, to find out how much louder 20 people talking would be than one person talking. Suppose the sound of one person talking has a relative intensity of 80 decibels.

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