Midterm Review & Solutions

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midtermreviewsolutions

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Critical vocabulary for midterm

Can you define all these terms? Doing so should be excellent practice for the exam, as well as a chance to review topics we’ve focused on over the past six weeks.

Rational function

Exponential function

Logarithmic function

Asymptote

Zeroes

y-intercept

Logarithm

Inverse function

Logarithmic scale

Exponential growth

Exponential decay

Exponential growth rate

Exponential decay rate

Continuously compounded interest

Solutions to Midterm Exam Review

1. 3

2. -2

3. -4

4. 4

5. 2

6. 3

7. 0

8. 3

9. 2

10. 0

11. \frac{-39}{4}

12. -48

13. 4 \log 2-8=\log 16-8

14. x=\frac{11}{4}

15. x=\frac{18}{11}

16. x\le7

17. x<-1

18. x=\{\frac{-1}{3},1\}

19. x=5

20. x=2

21. x\ge 4

22. x=(3,103)

23. x=(1.5,5)

25. x=8

26. x=-3+4\sqrt{2}

27. x=\frac{\ln \frac{1}{2}}{2}

28. x=-\ln 4

29. x=\log_5 3

30. x=\frac{\log_2 7}{\log_2 7-1}

31. x=\{ 0,\ln 4 \}

32. x=1

33. \frac{\ln 3}{0.2} hours

34. y=2^{x-2}-2

35. 10000\sqrt{10}

36. Logarithmic scales allow us to express a huge range of intensity using manageable numbers.

37. \log_2 9 is larger because 2^3=8, which is less than 9, and 5^3=125, which is greater than 30. So \log_2 9 must be more than 3 and \log_5 30 must be less than 3.

38. 

39.  x-intercept at x=-996

40. a. Rational functions can have vertical asymptotes, horizontal asymptotes, slant asymptotes, and curvilinear asymptotes.

b. All exponential functions have horizontal asymptotes but no other asymptotes.

c. All logarithmic functions have vertical asymptotes but no other asymptotes.

41. 

42. 

43. Horizontal asymptote at y=2. Vertical asymptotes at x=2 and x=-3.

44. 

45. 

46. Horizontal asymptote at y=-4. Vertical asymptotes at x=2 and x=-2.