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Date: _______________
Course: ____________________
A2T Unit 8 - Exponential Functions - Review Problem Set
INSTRUCTIONS: Evaluate each expression.
1
15. g ( x )  2 x  ( x );g(4)
2
1. 3
1
16
1
16
1
2. 2
x5
1
16. g ( x )  ( 7 )2 ; g (10)
x
2
10000
1
3
Write
each expression with only one positive
3. 8
exponents and express the answer in simplest form.
2
The variables are not equal to zero.
4. 5(3)
17. (27 x)3  3( x)1
5
59049x2
5. 8(2)3
a 3bc 3
64
)
18. (
abc 3
6. 5(0.1)2
c6
c
500
or( )6
1
6
a
a
7. 12(9) 2
1
x3 
36
19. ( 2 ) 5
b
8. (2  3)2
1
1
3 2
5 5
x
b
36
3
1
20. (2 x2 y 2 z 2 )(3x 3 y 3 z 1 )
9. (9  9) 4
3
10. 100
1
10

1
2
6 yz
x
Write each radical expression with only positive
exponents and express the answer in simplest form.
The variables are positive numbers.
3
21.
25x
3
1
2
2
11. 125 3
25
4
3
1 2. (12  )

3
2
1
1
64
Evaluate each function for the given value. Be sure
to check your work.
1
4
1
4
13. g (x )  x x ;g(4)
2


 1 
; g (3)
14. g (x )  
1 
 1  3 
x 

1
28
5x 2
22.
3
81 y 3
3 y5
3
2
y3
23. 12 64a7 b20
1
7
2
1
7
5
b(6412 a12 b 3 )or 2 2 a12 b 3
24.
1
6
6
32x8 y 3
4
3
1
2
5
6
4
3
32 x y or 2 x y
1
2
Write each power as a radical expression in simplest
form. The variables are positive numbers.
25. (2 y )
5
2
4 y2 2 y
1
26. (16 x8 y ) 2
4x 4 y
(a  2) 4
)
24
( 4 a  2 )3
8
a12b9 c 1
28. ( 6 3 ) 4
ab
3
27. (
ab 4 a2b2c
29. A. Sketch the graph of y  1.25x.
B. On the same set of axes sketch the graph of
y  0.80 x.
C. Under what transformation is the graph of
y  0.80 x the image of y  1.25x ?
Solve and check each equation.
30. x 2  36
1
6
1
3
31. a  4
64
1

2
32. b 2 
3
9
4
33. y 3  6  14
1
2
a2
34. 3  7  9
a
1
2
35. 4 x  2  10
3
2
36. 2(5) x  50
2
37. 7 x  72 x2
2
38. 2 x2  8x2
4
39. 0.10 x  102 x1
1
40. 3x1  27 x
1
2
41. 2  0.5x
1
42. Find the interest that has accrued on an
investment of $500 if interest of 4% per year is
compounded quarterly for a year.
$520.30
3. The label on a prescription bottle directs the
patient to take the medicine twice a day. The
effective ingredient of the medicine decreases
continuously at a rate of 25% per hour. If a dose of
medicine containing 1 milligram of the effective
ingredient is taken, how much is still present 12
hours later when the second dose is taken?
0.05mg
44. A sum of money that was invested at a fixed rate
of interest doubled in value in 15 years. The interest
was compounded yearly. Find the rate of interest to
the nearest tenth of a percent.
4.7%
45. A company records the value of a machine used
for production at $25000. As the machine ages its
value depreciates that is decreases in value. If the
depreciation is estimated 20% of the value of the
machine at the end of each year what is the
expected value of the machine after 6 years?
$6553.60