WorksheetsExponentials Test Review
Total questions: 68
Worksheet time: 3hrs 7mins
Name
Class
Date
1.
Write in exponential form
∛x⁷
∛x⁷
a)
x⁷∕ ³
b)
x3⁄7
c)
3x⁷
d)
7x³
2.
Write as a radical expression
y²⁄ ³
y²⁄ ³
a)
2y³
b)
√y³
c)
∛y²
d)
3y²
3.
Write as a radical expression
y¹⁄ ³
y¹⁄ ³
a)
∛y
b)
y³
c)
√y
d)
1∕ 3y
4.
Simplify:
a)
2
b)
8
c)
16
d)
32
5.
Simplify the following expression:
a)
2
b)
4
c)
16
d)
64
6.
Simplify:
a)
2
b)
4
c)
16
d)
64
7.
85/3
a)
64
b)
32
c)
16
d)
24
8.
1252/3
a)
5
b)
25
c)
75
d)
5
9.
644/3
a)
256
b)
8
c)
84
d)
2
10.
45/2 = ?
a)
10
b)
16
c)
32
d)
64
11.
a)
A
b)
B
c)
C
d)
D
12.
a)
A
b)
B
c)
C
d)
D
13.
.
a)
A
b)
B
c)
C
d)
D
14.
Rewrite in radical form.
a)
A
b)
B
c)
C
d)
D
15.
2
a)
C
b)
A
c)
V
d)
E
16.
a)
64
b)
8
c)
2
d)
32
17.
Evaluate 813/4
a)
1/3
b)
3
c)
27
d)
243
18.
Simplify:
a)
8x9
b)
8x3
c)
8x4√x
d)
8x3√x
19.
Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.
a)
y=6(0.14)x
b)
y=6(1+14)x
c)
y=6(1.14)x
d)
y=6(0.86)x
20.
What type of function is y = 7(5/4)x?
a)
Exponential Growth
b)
Exponential Decay
c)
Linear
d)
None of the above
21.
Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)6
A=1200(.85)6
a)
Growth
b)
Decay
22.
What is a, the initial amount, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
23.
A 78 gram sample of Uranium loses half of its mass each year. What is the exponential equation?
a)
y=78(0.5)x
b)
y=78(1.5)x
c)
y=78(2)x
24.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
25.
Is this exponential growth or decay?
a)
Growth
b)
Decay
c)
Linear
26.
What does the a in y=a(1+r)x represent?
a)
Time
b)
Rate
c)
Slope
d)
Initial Amount
27.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
28.
What type of function is f(x)=2(1/7)x ?
a)
Exponential Growth
b)
Linear
c)
Exponential Decay
d)
None of the Abovee
29.
What is the decay rate in the following model?
A=1200(.85)6
a)
1200
b)
.15
c)
.85
d)
6
30.
What is the decay factor in the following model?
A=1200(.85)6
A=1200(.85)6
a)
1200
b)
-.15
c)
.85
d)
A
31.
Is this exponential growth or decay?
a)
Growth
b)
Decay
32.
What is r, the growth rate, for the function: f(x) = 300(1.16)x?
a)
300
b)
1.16
c)
.16
d)
x
33.
Is y = 5(1.04)x growth or decay?
a)
Growth
b)
Decay
34.
Is y = 4(.20)x growth or decay?
a)
Growth
b)
Decay
35.
The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?
a)
9766
b)
9006
c)
9765
d)
5433
36.
Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.
a)
y=5000(0.7)x
b)
y=30(5000)x
c)
y=5000(1.3)x
d)
y=5000xx
37.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
a)
$23,219.72
b)
$136.72
c)
$51,710.94
d)
$16,710.94
38.
Write the percent as a decimal.
4.3%
4.3%
a)
4.3
b)
.43
c)
.043
d)
4300
39.
Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 year?
a)
$827.52
b)
$831.10
c)
$839.45
d)
$846.80
40.
Your 3 year investment of $20,000 received 5.2% interest compounded annually. What is your total return?
a)
$23,285.05
b)
$3,285.05
c)
$2,385
d)
$32,285
41.
You borrowed $59,000 for 2 years at 11% which was compounded annually. What total will you pay back?
a)
$13,693.90
b)
$1,363.90
c)
$72,693.90
d)
$73,793.90
42.
Karla invested $1,000 in savings bonds. If the bonds earn 6.75% interest compounded semi-annually, how much total will Karla earn in 15 years?
a)
$1,584.62
b)
$2,651.39
c)
$2,706.86
d)
$1,825.10
43.
Emily would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years.
a)
$15,415.94
b)
$15,683.28
c)
$15,927.56
d)
$16,109.05
44.
Monthly means how many times a year?
a)
4
b)
12
c)
52
d)
365
45.
Principal: $999
Interest Rate: 5.45%
Time: 19 years
Compounded Quarterly
State the future account balance.
Interest Rate: 5.45%
Time: 19 years
Compounded Quarterly
State the future account balance.
a)
$2794.10
b)
$2738.11
c)
$2774.98
d)
$2807.11
46.
Principal: $5000
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.
Interest Rate: 3.75%
Time: 25 years
Compounded Monthly
State the future account balance.
a)
$12712.31
b)
$12,749.30
c)
$12,657.59
d)
$12550.84
47.
Change 6.75% to a decimal.
a)
67.5
b)
.675
c)
675
d)
.0675
48.
Semi-Annually means how many times a year?
a)
4
b)
2
c)
1
d)
6
49.
What is the simplified for of 3a4b-2c3?
a)
(81a4c3)/(b2)
b)
(81a4)/(b2c3)
c)
(3a4)/(b2c3)
d)
(3a4c3)/(b2)
50.
What is -a-2 if a =-5?
a)
-25
b)
25
c)
-1/25
d)
1/25
51.
What is the simplified form of (-3x3y2)(5xy-1)?
a)
(-15x3)/(y2)
b)
-15x3y2
c)
-15x4y1
d)
15x4y1
52.
What is the simplified form of -9m-2n5 ⋅ 2m-3n-6?
a)
-18m5n
b)
(-18)/(m5n)
c)
(-18m6)/(n30)
d)
-18m6n30
53.
Multiply
-7x2y (2x4)
-7x2y (2x4)
a)
-14x6
b)
14x6y
c)
-14x6y
d)
-14x6y2
54.
(2⁸)²
a)
2¹⁶
b)
2¹⁰
c)
2⁶
d)
2⁴
55.
5³⋅5⁴
a)
5⁷
b)
5⁻¹
c)
5¹²
d)
5
56.
Anything raised to a power of zero is always:
a)
0
b)
1
c)
itself
d)
negative
57.
n²⋅n⁴⋅n⁵
a)
n¹¹
b)
n⁴⁰
c)
n¹³
d)
n²²
58.
7⁰
a)
1
b)
7
c)
0
d)
-7
59.
Fill in the blank with the correct exponent to make the statement true.
316 = (38)(3_)
316 = (38)(3_)
a)
2
b)
8
c)
4
d)
1
60.
(x6)3
a)
x9
b)
x2
c)
x6
d)
x18
61.
(3x4)(4x2)
a)
7x6
b)
12x6
c)
7x8
d)
12x8
62.
(x5y3)4
a)
x9y7
b)
x9y12
c)
x20y12
d)
x20y7
63.
(-6xy3)(x4y2)
a)
-6x5y5
b)
-6x4y5
c)
6x5y5
d)
6x4y6
64.
(x2y3)2(xy)
a)
x4y6
b)
x5y7
c)
x4y5
d)
x5y6
65.
Simplify the expression shown. Your answer should contain only positive exponents.
a)
b)
c)
d)
66.
Simplify the expression shown. Your answer should contain only positive exponents.
a)
b)
c)
d)
67.
Simplify the expression shown. Your answer should contain only positive exponents.
a)
4x6
b)
y4
c)
32x5y4
d)
-4x7y3
68.
a)
b)
c)
1
d)
0
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