Algebra II Review 4/1-4
Does the function show growth or decay?
1. f(x) = 0.4x
2. f(x) = 1.2(2/5)x
5. f(x) = 5.1x
6. f(x) = 0.3(1/4)x
3. f(x) = 7/8(1.1)x
7. f(x) = 21(9/2)x
4. f(x) = 50(1+ 0.04)x
8. f(x) = 30(1 – 0.04)x
9. Gina buys a car for $13,500. Its value will decrease by 15% per year. Write an exponential function
to model the value of the car. Graph the function on the graphing calculator and use the graph to
predict when the value of the car will be $3000.
10. John invests $1500 in an account which will increase by 4% per year. Write an exponential function
to model the value of the investment. Graph the function on the graphing calculator and use the
graph to predict when the value of the investment will be $3000.
Write each exponential equation in logarithmic form.
11. 161/4 = 2
12. 16-0.5 = 1/4
13. 35 = 243
15. (1/3)-3 = 27
16. 91.5 = 27
17. 104 = 10,000
14. 90 = 1
18. 6-1 = 1/6
Write each logarithmic equation in exponential form.
19. log1/4 64 = -3
20. log81 1/3 = -1/4
21. log2 16 = 4
23. log0.6 0.36 = 2
24. log2 128 = 7
25. log8 64 = 2
22. log 10 = 1
26. log4 (1/16) = -2
27. Use the given x-values to graph f(x) = (3/4)x.
State the inverse function.
Graph the inverse function.
x
y
-1
-2
-1
0
1
2
3
28. Use the given x-values to graph f(x) = (1/5)x.
State the inverse function.
Graph the inverse function.
x
y
-1
0
4
4
3
3
2
2
1
1
0
1
2
3
4
-2
-1
0
-1
-1
-2
-2
1
1
2
2
Express as a single logarithm. Simplify if possible. Show your work.
29. log5 252
30. log2 8 + log2 16
31. log 10 – log 0.1
32. log4 128 – log4 8
33. log2 12.8 + log2 5
34. log3 272
35. log3 3
36. Log4 1
37. Log1/4 4
log9 99
38. log1/6 1
39. 9
40. 5log5 0.05
3
3
4
Evaluate.
41. log7 49
44. log 0.01
42. log0.5 0.25
45. log2 1
43. log12 (1/12)
46. log4 64
Answers:
1. decay
5. growth
2. decay
6. decay
3. growth
7. drowth
4. growth
8. decay
9. y = 13500(0.85)x; x is about 9 years
10. y = 1500(1.04)x; x is about 17 ½ years
11. log16 2 = ¼
15. log1/3 27 = -3
12. log16 ¼ = -0.5
16. log9 27 = 1.5
13. log3 243 = 5
17. log 10,000 = 4
14. log9 1 = 0
18. log6 1/6 = -1
19. (1/4)-3 = 64
23. (0.6)2 = 0.36
20. (81)-1/4 = 1/3
24. 27 = 128
21. 24 = 16
25. 82 = 64
22. 101 = 10
26. 4-2 = 1/16
27. Use the given x-values to graph f(x) = (3/4)x.
State the inverse function.
Graph the inverse function.
x
y
-1
1.3
-2
39. 4
45. 1
51. 2
54. -2
-1
40. 7
46. 0
0
1
1
0.75
2
0.56
3
0.42
28. Use the given x-values to graph f(x) = (1/5)x.
State the inverse function.
Graph the inverse function.
x
y
-1
5
0
1
4
4
3
3
2
2
1
1
0
1
2
3
4
-2
-1
0
-1
-1
-2
-2
41. 2
47. -1
52. 2
55. 0
42. 2
48. 0
43. 6
49. 99
53. -1
56. 3
1
0.2
1
2
0.04
2
44. 6
50. 0.05
3
3
0.008
4