1. Chapter 4 Review Game Rules
I will put up calculator and no calculator problems. If caught using a calculator on a no calculator problem, your team loses all of its points.
Each member of the team with the most points at the end of class with get a homework pass.

2. Simplify the following without a radical symbol
#1: No Calculator
Simplify the following without a radical symbol

3. #1: Answer
(8x3y12z9)1/3
81/3 ∙ x3/3 ∙ y12/3 ∙ z9/3
2xy4z3

4. Evaluate the following
#2: No Calculator
Evaluate the following

5. #2: Answer
1/16

6. #3: No Calculator
Write an equivalent equation for A = BC2 using ln A in terms of ln B and lnC.

7. #3: Answer
lnA = lnB + 2lnC

8. Solve ln t = 0.14 to the nearest hundredth.
#4: Calculator
Solve ln t = 0.14 to the nearest hundredth.

9. #4: Answer
e0.14 = 1.15

10. #5: Calculator
A bank account starts with $4800 with an interest rate of 6.75% compounded monthly. How much money (to the nearest penny) is in the account at the end of five years?

11. #5: Answer
4800( /12)12*5 = $

12. #6: Calculator
In 1989, Vermont had a population of 567,000 people. The state was growing at 1.2% annually. At this rate of growth, in what year would Vermont reach a population of 600,000 people?

13. #6: Answer
567000*e0.012x =
e0.012x = 600/567
ln (600/567)/0.012 = x
x = 4.71 years
= 1994

14. #7: No Calculator
Between what two integers is log387?

15. Between 4 and 5 #7: Answer because 34 = 81 and 35 = 243,

16. #8: No Calculator
Evaluate the following:
-3/4

17. #8: Answer
8/27

18. #9: No Calculator
Evaluate the following logarithm.

19. #9: Answer
1/3

20. #10: Calculator
Solve for x to the nearest hundredth.
32x = 38

21. #10: Answer
Log3 38 = 2x
Log3 38 = x 2
x = 1.66

22. #11: Calculator
Polonium-200 has a half-life of 140 days. How many grams (to the nearest hundredth) would be left after one year if you started with 200 grams?

23. #11: Answer
y = abx
y = 200(.5)365/140
y= 32.82g

24. #12: Calculator
Solve for n to the nearest thousandth.
21(12)n = 5556

25. #12: Answer n = 2.245 12n = 5556/21 log12(5556/21) = n

26. #13: No Calculator log480 – log45
Evaluate the following logarithm using properties learned in this chapter.
log480 – log45

27. #13: Answer
log4(80/5)
= log416
= log4(42)
= 2

28. #14: No Calculator logt x = logt s – 3logt r
Write the following equation without logarithms.
logt x = logt s – 3logt r

29. #14: Answer
logtx = logt (s/r3)
x = s/r3

30. #15: No Calculator
Use the fact that log54 = to help calculate the following logarithm.
log520

31. #15: Answer
log5(5*4) = log55 + log54 = =

32. #16: Calculator
Solve the following equation for x to the nearest thousandth.
5x = 2.413

33. #16: Answer
log = x
log = x
log 5
x = 0.547

34. #17: Calculator
A savings account is started with $10,000. It is continuously compounded at 9.75% interest. How many years (to the nearest tenth) will it take for the account balance to triple in value?

35. t = 11.3 years #17: Answer 30000 = 10000e.0975t 3 = e.0975t
ln 3 = .0975t
t = ln 3/ .0975
t = 11.3 years

36. #18: Calculator
Solve the following equation for b to the nearest thousandth.
logb 35 = 3

37. #18: Answer
b3 = 35
b = 351/3
b = 3.271

38. #19: No Calculator
Simplify the following expression

39. #19: Answer
ln e-3 = -3

40. #20: No Calculator
Write the following as one logarithm.

41. #20: Answer
log3b3/2 - log3c4
log3 (b3/2/c4)

42. Simplify the following expression
#21: No Calculator
Simplify the following expression

43. #21: Answer
log6 (1/63)
=log66-3
= -3

44. f(x) = log6x #22: No Calculator
Write an equation for the inverse of the following function.
f(x) = log6x

45. #22: Answer
f-1(x) = 6x

46. #23: Calculator
$800 is put in a savings account at the birth of a child. The account earns 10% continuously compounded. How much money is in the account (to the nearest penny) on the child’s 21st birthday if no money is deposited or withdrawn?

47. #23: Answer
y = 800e0.10*21
y = $

48. #24: Calculator
Calculate the following log to the nearest tenth.
log319

49. #24: Answer
log 19 = ln 19
log ln 3
2.7

50. #25: Calculator
A biologist finds the number of species S on an island is related to the area A of the island. Use the following equation to determine the area of the island (to the nearest square mile) if there are 420 species on the island.
S = 28.3A0.39

51. #25: Answer
420 = 28.3A0.39 (420/28.3) = A39/100 (420/28.3)100/39 = A A = 1009 mi.2

52. #26: Calculator
Find the domain and range of the following function:
g(x) = 8x – 7

53. Domain: All Real Numbers Range: All Real Numbers > -7
#26: Answer
The graph of 8x - 7 is the graph of 8x shifted
down seven units. This means the
horizontal asymptote is also shifted down
seven units.
Domain: All Real Numbers
Range: All Real Numbers > -7