Algebra II w/ Trig.
Test #3 Review (8-1 – 8-4)
With Solutions
Without graphing, determine whether each exponential equation represents growth or decay.
1. y = 72(1.6)2
2. y = 24(.8)x
3. y = 3 (6/5)x
4. y = 7(2/3)x
Growth
decay
growth
decay
Sketch each using transformations (plot 2 points & the horizontal asymptote).
5. y = 2x – 3 – 4
6. y = -3x + 2
7. y = 2(3)x +2 + 1
8. y = (2/3)x + 3 + 3
9. y = -.5(2)x
Write an exponential function for the graph containing the following points.
10. (0, 2) (1, 1.3)
11. (1, 10) (3, 27)
12. (-1, 12.5) (4, 4.096)
x
x
x
y = 2(.65) or y = 2(13/20)
y = 6.1(1.64)
y = 10(.8)x
13. Suppose $500 is invested at 6% annual interest compounded continuously. W hat will the investment be worth
after 10 years? $911.06
14. An organism of a certain type can grow at a rate of 37.44%. If 30 organisms are present now, how many will
be present after 3 days? 92.24 organisms
15. Dave bought a car for $8400 8 years ago. If the car depreciated at a rate of 5.09%, what is the value now?
$5530.64
Write in logarithmic form.
16. 33 = 27
17. 53 = 125
log327 = 3
log5125 = 3
Write in exponential form.
18. 25 = 32
log232 = 5
19. 274/3 = 81
log2781 = 4/3
20. 4-2 = 1/16
log4(1/16) = -2
23. log8 4 = 2/3
24. log9 3 = ½
24. log 0.001 = -3
82/3 = 4
91/2 = 3
10-3 = 0.001
26. log5 25
2
27. log3 9
2
28. log14 196
2
29. log2 (-16)
undefined
31. log15 15x = y
y-1 = 15x – 1
32. log12 x = y
y-1= 12x
33. log 3x
34. log2 (5a)3
35. log12
36. log4 (√𝑎b2c4)3
37. log3
log 3 + log x
log2 5 + 3log2 a
√6
21. log5 125 = 3
22. Log1.5 3 =-1/2
53 = 125
1.5-1/2 =
Evaluate.
25. log3 27
3
Find the inverse.
30. log7 x = y
y-1 = 7x
Expand.
√6
3
Write as a single logarithm.
38. log6 x + log6 9
4𝑥 −2 √𝑦
3𝑧 7
𝑎2 𝑏3
4𝑐 4
35. log12 4 – 2 log12 x + ½ log12 y – log12 3 – 7log12 z
36. 3/2 log4 a + 6log4 b + 12log4 c
37. 2log3 a + 3log3 b – log3 4 – 4log3 c
39. log6 (3m + 7) – log6 m
40. log8 48 – 2log8 w
log6 9x
3𝑚+7
log6 𝑚
log8 𝑤 2
41. log2 x + 2/3 log24 – 3 log2y – ylog2z
42. log7 x + ½ log7 y – log7 3
43. 3log 10 – 3log a + 4log b
log2
3
√16𝑥
𝑦3𝑧4
Evaluate.
44. log12 6 + log12 24
log7
2
𝑥 √𝑦
3
45. 2log2 8 – 3log2 4 0
48
log
1000𝑏4
𝑏3