Algebraic Exponents & Exponential Functions Chapter Questions
1.
How can you tell the difference between a linear and an exponential relationship?
2.
Explain the difference between growth factors and growth rates.
3.
Explain the difference between decay factors and decay rates.
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Algebraic Exponents & Exponential Functions Chapter Problems
Exponential Growth Introduction
Classwork
1. The drama club wants to make confetti even faster. Now they decide to take one piece of paper and cut it into fourths.
Then they stack the four pieces and cut them into fourths. They repeat this process creating smaller and smaller
pieces of paper.
a.
Create a table showing the number of cuts from 1 to 5 and the pieces of confetti.
b.
How many pieces of confetti after 10 cuts?
c.
How is this process different than when the paper was cut in halves and thirds?
2. For each expression below, identify the exponent and the base and write the answer.
a. 75
b. 113
c. 94
d. 105
e. 47
3. Write each expression in exponential form.
a. 4 x 4 x 4 x 4 =
b. 7 x 7 x 7 x 7 x 7 x 7 =
c. 3 x 3 =
d. 9 x 9 x 9 x 9 x 9 =
e. 12 x 12 x 12 x 12 =
4. Write each expression in standard form.
a.
b.
c.
d.
e.
83 =
56 =
27 =
93 =
144 =
5. Explain how the meanings of 24, 42 and 2 x 4 differ.
6. Find:
a.
b.
c.
Five squared
Two to the fifth power
Nine cubed
7. Given 7x = 343, what is the value of x?
8. Given 6x = 1296, what is the value of x?
9. Given 3x = 729, what is the value of x?
10. Given x6 = 4096, what is the value of x?
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11. Given x3 = 1000, what is the value of x?
12. Given x2 = 196, what is the value of x?
Write the product as a power.
13. 2 * 2 * 2 * 2
14. 8 * 8 * 8 * 8 * 8 * 8 * 8
15. m * m * m * m * m * m
Write using exponents.
16. 5 squared
17. The fifth power of 7
18. P to the sixth
Evaluate each expression.
19. 24 =
21. 92 =
20. 33 =
22. 106 =
Homework
23. The drama club wants to make confetti even faster again. Now they decide to take one piece of paper and cut it into
fifths. Then they stack the five pieces and cut them into fifths. They repeat this process creating smaller and smaller
pieces of paper.
a.
Create a table showing the number of cuts from 1 to 5 and the pieces of confetti.
b.
How many pieces of confetti after 10 cuts?
c.
How is this process different than when the paper was cut in halve, thirds, and fourths?
24. For each expression below, identify the exponent and the base and write the answer.
a.
b.
c.
d.
e.
35
82
104
123
67
25. Write each expression in exponential form.
a. 5 x 5 x 5 =
b. 2 x 2 x 2 x 2 x 2 x 2 =
c. 10 x 10 x 10 x 10 =
d. 8 x8 =
e. 1 x 1 x 1 x 1 x 1 x 1 =
26. Write each expression in standard form.
a. 124 =
b. 47 =
c. 105 =
d. 36 =
e. 810 =
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27. Explain how the meanings of 35, 53 and 3 x 5 differ.
28. Find:
a.
Eight to the fourth power
b.
Four cubed
c.
Twelve squared
29. Given 5x = 625, what is the value of x?
30. Given 9x = 81, what is the value of x?
31. Given 2x = 256, what is the value of x?
32. Given x7 = 10,000,000 what is the value of x?
33. Given x4 = 2401, what is the value of x?
34. Given x4 = 81, what is the value of x?
Write the product as a power.
35.
36.
37.
38.
39.
10 * 10 * 10 * 10 * 10
6*6*6
n*n
y*y*y*y*y
94 * 94 * 94 * 94
Write using exponents.
40. q squared
41. seven to the fourth
42. three to the fifth
43. five cubed
44. two to the sixth
Evaluate each expression
45. 53=
46. 340 =
47. 561=
48. 82 =
49. 63 =
Exponential Growth v. Linear Growth
Classwork
Write whether the equation shows a linear growth or an exponential growth.
50. 𝑦 = 2𝑥
51. 𝑦 = 23 + 𝑥
52. 𝑦 = 3𝑥 + 7
53. 𝑦 = 3𝑥 2
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54. 𝑦 = 4𝑥 3
Does the graph show an exponential growth or a linear growth?
55. __________________
56. __________________
57. __________________
Do the tables show an exponential growth or a linear growth?
58. __________________
59. __________________
60. __________________
Simplify.
61.
62.
63.
64.
65.
m2 * m5 =
c5 * c4 * c2 =
y3 * y3 =
5z3 * z5 =
6p8 * 4p3=
66.
67.
68.
69.
70.
b2 * b =
d4 * d3 * d
x3 * x * x5 * x4 =
(3xy2)(8xy4) =
p3 * q4 * q7 =
Homework
Write whether the equation shows a linear growth or an exponential growth.
71. 𝑦 = 2𝑥 + 3
72. 𝑦 = 1.2𝑥 2 + 4
73. 𝑦 = 1.2𝑥 + 32
74. 𝑦 = 4𝑥 + 1
75. 𝑦 = 2𝑥 3
Does the graph show an exponential growth or a linear growth?
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76. __________________
77. __________________
78. __________________
Do the tables show an exponential growth or a linear growth?
79. __________________
80. __________________
81. __________________
Simplify.
82.
83.
84.
85.
86.
v7 * v7 =
t * t8 * t10 =
–n7 * -6n8 =
-10z6 * 3z4 =
x2 * x6 =
87.
88.
89.
90.
91.
(-5u2v3)(4uv2) =
(-3j3k)(-5j2k2) =
54n * -2n3 =
a3 * c4 * c3 * a7 =
w8 * w7 =
Exponential Relationships in Tables, Equations and Graphs
Classwork
92. In the table below:
a.
What is the y intercept?
b.
What is the growth factor?
c.
What equation fits this data?
d.
Graph the data on a coordinate plane.
x
Y
0
1
1
3
2
9
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3
27
4
81
93. In the table below:
a. What is the y intercept?
b. What is the growth factor?
c.
What equation fits this data?
d. Graph the data on a coordinate plane.
x
Y
0
1
1
5
2
25
3
125
4
625
94. In the table below:
a. What is the y intercept?
b. Is there a growth factor? What type of relationship does the table show?
c.
What equation fits this data?
d. Graph the data on a coordinate plane. How does this graph differ from the first two examples?
x
Y
0
1
1
5
2
9
3
13
4
17
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95. You decide to start a garden at your house and plant Black-Eyed Susans. The next summer you notice that the
flowers had reproduced significantly and you wrote the following equation n = 5(4 t). In the equation n represents the
number of flowers after t time in years.
a. How many flowers did you plant the first year?
b. What is the growth factor of the Black-Eyed Susans in the garden?
c.
How many flowers will be in the garden after 4 years?
d. In how many years will there be over 5,000 plants in the garden?
96. The table below shows how a population of rabbits increases over several years.
a. Is the population linear or exponential or neither?
b. What is the starting population?
c.
Write an equation to represent the data in the table.
Year
Total rabbits
0
12
1
36
2
108
3
324
4
972
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97. The table below shows how a population of whales increases over several years.
a. Is the population linear or exponential or neither?
b. What is the starting population?
c.
Write an equation to represent the data in the table.
Year
Total whales
0
50
1
55
2
60
3
65
4
70
98. For each table below decide if the relationship is linear, absolute value, exponential or none of them. If it represents
one of them write the equation to represent the data.
Table A
Table B
Table C
X
y
x
y
x
Y
0
60
1
12
1
3
1
240
2
36
2
2
2
960
3
108
3
1
3
3840
4
324
4
0
4
15360
5
972
5
1
Table D
Table E
Table F
X
y
x
Y
x
Y
5
6.5
0
6
2
64
6
9
1
7
3
512
7
11.5
2
10
4
4096
8
14
3
15
5
32768
9
16.5
4
22
6
262144
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Simplify.
99. a9 ÷ a4 =
100.
102.
x21 ÷ x5 =
103.
101.
107
103
104.
1321
137
10𝑎12 ÷ 5𝑎3
20𝑥 4
4𝑥 2
Homework
105.
In the table below:
a. What is the y intercept?
b. What is the growth factor?
c.
What equation fits this data?
d. Graph the data on a coordinate plane.
106.
X
Y
0
1
1
4
2
16
3
64
4
256
In the table below:
a. What is the y intercept?
b. What is the growth factor?
c.
What equation fits this data?
d. Graph the data on a coordinate plane.
X
Y
0
1
1
7
2
79
3
343
4
2401
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107.
In the table below:
a. What is the y intercept?
b. Is there a growth factor? What type of relationship does the table show?
c.
What equation fits this data?
d. Graph the data on a coordinate plane. How does this graph differ from the first two examples?
X
Y
0
9
1
9.5
2
10
3
10.5
4
11
108.
You decide to start a garden at your house and plant Black-Eyed Susans. The next summer you notice that the
flowers had reproduced significantly and you wrote the following equation n = 8(4 t). In the equation n represents the
number of flowers after t time in years.
a. How many flowers did you plant the first year?
b. What is the growth factor of the Black-Eyed Susans in the garden?
c.
How many flowers will be in the garden after 4 years?
d. In how many years will there be over 5,000 plants in the garden?
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109.
The table below shows how a population of rabbits increases over several years.
a. Is the population linear or exponential or neither?
b. What is the starting population?
c.
110.
Write an equation to represent the data in the table.
Year
Total rabbits
0
50
1
150
2
450
3
1350
4
4050
The table below shows how a population of whales increases over several years.
a. Is the population linear or exponential or neither?
b. What is the starting population?
c.
Write an equation to represent the data in the table.
Year
Total whales
0
250
1
278
2
306
3
334
4
362
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111.
For each table below decide if the relationship is linear, absolute value, exponential or none of them. If it
represents one of them write the equation to represent the data.
Table A
Table B
Table C
X
y
x
y
x
y
0
12
1
55
0
15
1
9
2
275
1
16
2
6
3
1375
2
19
3
3
4
6875
3
24
4
0
5
34375
4
31
Table D
Table E
Table F
X
y
x
y
x
y
5
2
0
10
3
864
6
1
1
30
4
5184
7
0
2
90
5
31104
8
1
3
270
6
186624
9
2
4
810
7
1119744
Simplify
112.
113.
114.
𝑧 14
𝑧8
115.
𝑚20 ÷ 𝑚18
116.
𝑠 20
𝑠 15
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117.
10473
1027
434 ÷ 48
30𝑥 37
5𝑥 12
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Growth Factors and Growth Rates
Classwork
118.
What is the growth factor in each of the following exponential tables below?
Table A
Table B
Table C
X
y
x
y
x
Y
0
4
1
1.8
2
61.25
1
9.6
2
3.24
3
214.38
2
23.04
3
5.83
4
750.31
3
55.296
4
10.50
5
2626.09
4
132.71
5
18.90
6
9191.33
Table D
Table E
Table F
X
Y
x
y
x
Y
3
103.8
0
13
1
31.2
4
488.0
1
15.6
2
121.7
5
2293.5
2
18.72
3
474.6
6
10779.2
3
22.46
4
1850.8
7
50662.3
4
26.96
5
7217.9
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119.
Fill in the table below with the missing growth factors and growth rates.
Growth
factor
Growth rate
1.05
5%
25%
7%
1.42
2.5
1.20
50%
42%
1.43
120.
If you invest $750 at a yearly interest rate of 7%:
a. What is the growth factor?
b. How much money will you have after 6 years?
121.
If you invest $50 at a yearly interest rate of 3%:
a. What is the growth factor?
b. How much money will you have after 10 years?
122.
If you invest $1225 at a yearly interest rate of 4%:
a. What is the growth factor?
b. How much money will you have after 6 years?
Evaluate.
123.
(-10)2=
128.
(−1)5 =
124.
(−2)3 =
129.
(−10)7 =
125.
(−2)5 =
130.
(−4)4 =
126.
(−3)2 =
131.
(−7)0 =
127.
(−3)3 =
132.
(−8)1 =
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Homework
133.
What is the growth factor in each of the following exponential tables below?
Table A
Table C
X
Y
x
y
x
Y
0
3
1
4.2
2
5.29
1
5.1
2
17.6
3
12.17
2
8.67
3
74.1
4
27.98
3
14.74
4
311.2
5
64.36
4
25.06
5
1306.9
6
148.04
Table B
134.
Table E
Table D
Table F
X
Y
X
y
x
Y
3
31.25
0
6
1
13
4
78.13
1
20.4
2
16.9
5
195.31
2
69.36
3
21.97
6
488.28
3
235.82
4
28.56
7
1220.7
4
801.8
5
37.13
Fill in the table below with the missing growth factors and growth rates.
Growth factor
Growth rate
1.50
50%
1.45
1.07
4%
88%
1.23
1.40
28%
30%
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135.
If you invest $900 at a yearly interest rate of 4%:
a. What is the growth factor?
b. How much money will you have after 7 years?
136.
If you invest $2000 at a yearly interest rate of 7%:
a. What is the growth factor?
b. How much money will you have after 4 years?
137.
If you invest $505 at a yearly interest rate of 5%:
a. What is the growth factor?
b. How much money will you have after 10 years?
Evaluate.
138.
(−6)2 =
143.
(−10)9 =
139.
(−6)3 =
144.
(−7)0 =
140.
(−3)4 =
145.
(−10)8 =
141.
(−3)5 =
146.
(−6)1 =
142.
(−5)5 =
147.
(−4)3 =
Exponential Decay
Classwork
148.
You have a bag of 500 pieces of candy and you eat a third of the pieces a day.
a. Create a table showing the candy remaining for days 0-8.
b. What is the y-intercept?
c.
What is the decay factor?
d. What equation matches this situation?
149.
You have another bag of candy with 700 pieces and you eat a fourth of the pieces a day.
a. Create a table showing the candy remaining for days 0-8.
b. What is the y-intercept?
c.
What is the decay factor?
d. What equation matches this situation?
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150.
Fill in the table below with the missing decay factors and decay rates.
Decay factor
Decay rate
0.85
15%
0.50
0.25
30%
45%
0.90
0.05
90%
8%
Simplify.
151.
(x4)3=
156.
(569)20=
152.
(y2)5=
157.
(4318)3=
153.
(c3)2=
158.
(w8)60=
154.
(22)8=
159.
(123)9=
155.
(36)7=
160.
(z5)6=
Homework
161.
You have a bag of 850 pieces of candy and you eat half of the pieces a day.
a. Create a table showing the candy remaining for days 0-8.
b. What is the y-intercept?
c.
What is the decay factor?
d. What equation matches this situation?
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162.
You have another bag of candy with 1,000 pieces and you eat a fifth of the pieces a day.
a. Create a table showing the candy remaining for days 0-8.
b. What is the y-intercept?
c.
What is the decay factor?
d. What equation matches this situation?
163.
Fill in the table below with the missing decay factors and decay rates.
Decay factor
Decay rate
0.45
55%
0.03
0.65
28%
72%
0.32
0.48
53%
40%
Simplify.
164.
(163)9=
169.
(t9)8=
165.
(126)3=
170.
(r7)7=
166.
(x10)7=
171.
(33)2=
167.
(104)8=
172.
(q8)3=
168.
(a6)7=
173.
(5412)3=
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Rules for Exponents
Classwork
174.
Complete each equation for the missing value:
a. (52)(55) = 5?
h.
59 ?
=5
56
i.
95
= 9?
98
j.
124 ÷ 126 = 12?
k.
108 ÷ 10? = 103
l.
2?
= 24
23
b. (127)(123) = 12?
c.
(3-2)(35) = 3?
d. (49)(4-3) = 4?
e. (54)(5?) = 512
f.
(107)(10?)(10-6) = 103
g. 34 ÷ 32 = 3?
175.
Simplify.
a. (4m5)2=
k. 3-4=
b. (-4z2)3=
l.
c. (a2b3)4=
m. 7-1=
d. (-2x2y3)5
n.
e. (2x3)4=
o. 11m-5=
(-4)-3=
(-3)-2=
(-3h3)5=
p. 2a-3=
g. (-4b3)3=
q. 7s-4=
f.
h.
(5a3)5=
r.
7s-4t2=
i.
(3x2y4)4=
s. n-5v2=
j.
(-j7)2=
t.
5-2p-1=
a. (122)(127) = 12?
f.
(11-6)(11?)(118) = 105
b. (25)(22) = 2?
g. 77 ÷ 73 = 7?
Homework
176.
c.
Complete each equation for the missing value:
(5-3)(55) = 5?
d. (158)(15-5) = 4?
1110
h.
= 11?
116
e. (67)(6?) = 615
i.
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j.
177.
26
= 2?
210
k.
136
= 132
13?
l.
5? ÷ 56 = 53
Simplify.
a. (-3r)3=
k. 4-2=
b. (3y2)5=
l.
c. (-2r5s2)6=
m. (-5)-2=
(-x)-2=
d.
(xy2)5=
n. 78-1=
e.
(-a2b3)3=
o. 5x-4=
f.
(-2r2s)4=
p. x-7=
g.
(4uv5)3=
q. 7ab-2=
h.
(c3)2=
r.
i.
(-d5)2=
s. 3s-2=
j.
(4x6y2)5=
t.
r-4s2=
x-5y7=
Unit Review
Multiple Choice– Choose the correct answer for each question.
1.
Find three cubed.
a. 3 x 2 = 6
c.
b. 3 x 3 = 9
d. 3 x (3 x 3 x 3) = 81
3
2
3 x 3 x 3 = 27
4
2. Expressed in simplest form, (3x )(3y2) (4x ) is equivalent to:
12 4
a. 36x y
12 4
c.
108x y
d.
108x y
a. 36
c.
216
b. 3
d. 4
7 4
b. 36x y
7 4
3. Given 6x = 216, find x.
4. In the equation y = 5(2x), what value does the 2 represent?
a. y-intercept
c.
b. starting value
d. growth rate
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5. The expression 3 –2 • 3-6 is equivalent to:
a. 312
c.
3-8
b. 3-12
d. 38
6. Given the equation y = 4(2x) if x = 4, what is the value of y?
a. 12
c.
64
b. 32
d. 8
7. Which of the following equations shows a linear relationship?
a. 𝑦 = 𝑥 2
c.
𝑦 = 3𝑥 2
b. 𝑦 = 2𝑥 + 2
d. 𝑦 = 4𝑥 3 + 1
8. What is the y intercept of the following relationship?
x
1
2
3
4
5
y
9
27
81
243
729
a. 3
c.
0
b. 15
d. 5
9. What is the y intercept of the following relationship?
x
1
2
3
4
y
11
121
1331
14641
a. 0
c.
10
b. 1
d. 11
10. What is the growth factor in the following relationship?
x
2
3
4
5
y
11.56
39.304
133.6336
454.35424
a. 3
c.
3.4
b. 3.2
d. 5.78
11. If the growth rate is 10%, what is the growth factor?
a. 10
c.
1.01
b. 1.1
d. 100
12. If the growth factor is 1.6, what is the growth rate?
a. 6%
c.
b. 60%
d. 160%
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13. What is the equation for this table?
x
0
1
2
3
4
y
20
26
33.8
43.94
57.122
a. y = 1.3x
c.
y = 20(1.3x)
b. y = 1.3(20x)
d. x = 1.3y
14. Identify the decay factor in the following table.
x
0
1
2
3
4
y
900
300
100
33.33
11.11
a. 900
c.
-3
b. 3
d. 1/3
15. In a science e x p e r i m e n t , the a m o u n t o f b a c t e r i a d e c r e a s e d e a c h d a y .
below shows the a m o u n t o f b a c t e r i a that remained at the start of work on successive days.
Day
1
Fractional Part of the
bacteria remaining
1
2
1
4
1
3
8
Which fractional part of the rock will remain at noon on day 6?
2
a.
b.
1
128
1
64
c.
d.
1
14
1
12
Short Constructed Response – Write the correct answer for each question.
16. Explain how the meanings of 42, 24 and 4∙2 differ.
17. Create an exponential relationship and explain what the growth factor is for the relationship.
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The table
18. Suppose there is an initial rabbit population in the forest of 5,000 deer. The growth factor for the population is 1.2 per
year. How large will the deer population be in year 4?
19. What will y equal if x equals 6 in the equation y = 15(2.1 x)?
20. What kind of growth does this table show?
X
0
1
2
3
4
y
5
10
20
40
80
Extended Constructed Response - Solve the problem, showing all work.
21. Given the following table:
a. Explain why the relationship is exponential.
b. Identify the:
i. Growth factor
ii. Growth rate
iii. y intercept
c. Graph the relationship.
d. Write the equation.
X
3
4
5
6
y
39.30
133.63
454.35
1544.80
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Algebraic Exponents & Exponential Functions Chapter Problems Answer Key
Classwork
4.
a. 8●8●8
1
b. 5●5●5●5●5●5
a.
1
4
c. 2●2●2●2●2●2●2
2
16
d. 9●9●9
3
64
e. 14●14●14●14
4
256
5
1024
5. 24= 2●2●2●2 =16, 42 =4●4 =16, 2●4 =8
6.
a. 25
b. 32
b. 1048576
c. 8
c.
7. 3
number
of cuts
fourths
halves
thirds
1
4
2
3
2
16
4
9
3
64
8
27
4
256
16
81
5
1024
32
243
8. 4
9. 6
10. 4
11. 10
12. 14
13. 24
14. 87
15. m6
2
16. 52
a. exponent 5, base 7, 16807
17. 75
b. exponent 3, base 11, 1331
18. P6
c. exponent 4, base 9, 6561
19. 16
d. exponent 5, base 10, 100000
20. 27
e. exponent 7, base 4, 16384
21. 81
3.
22. 1000000
a. 44
b. 76
c. 32
d. 95
e. 124
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c. 10●10●10●10●10
23.
d. 3●3●3●3●3●3
a.
e. 8●8●8●8●8●8●8●8●8●8
1
5
2
25
27. 35 = 3●3●3●3●3 = 243, 53 = 5●5●5 = 125, 3●5 = 15
3
125
28.
4
625
5
3125
a. 4096
b. 64
c. 144
b. 9765625
29. 4
c.
30. 2
Number
of Cuts
Fifths
Halves
Thirds
Fourths
1
5
2
3
4
2
25
4
9
16
3
125
8
27
64
31. 8
32. 10
33. 7
34. 3
35. 105
4
625
16
81
256
5
3125
32
243
1024
36. 63
37. n2
38. y5
24
39. 944
a. exponent 5, base 3, 243
40. q2
b. exponent 2, base 8, 64
41. 74
c. exponent 4, base, 10000
42. 35
d. exponent 3, base 12, 1728
43. 53
e. exponent 7, base 6, 279936
44. 26
25.
45. 125
a.
53
b. 26
c.
104
46. 1
47. 56
48. 64
d. 82
49. 216
e. 16
50. linear
26.
51. linear
a. 12●12●12●12
52. linear
b. 4●4●4●4●4●4●4
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53. exponential
85. -30z10
54. exponential
86. x8
55. linear
87. -20u3v5
56. exponential
88. 15j5k3
57. exponential
89. -108n4
58. linear
90. a10c7
59. exponential
91. w15
60. linear
92.
61. m7
a. 1
62. 2c10
b. 3
63. y6
c. y = 3(1x)
64. 5z8
d.
65. 24p11
66. b3
67. d8
68. x13
69. 24x2y6
70. p3q11
160
140
120
100
80
60
40
20
0
0
71. linear
72. exponential
1
a. 1
74. linear
b. 5
75. exponential
c. y = 5(1x)
76. exponential
d.
78. exponential
79. linear
80. exponential
81. exponential
82. v14
83. t19
3
4
5
2
3
4
5
93.
73. linear
77. linear
2
160
140
120
100
80
60
40
20
0
0
1
84. 6n15
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99. a5
94.
a. 1
100. x16
b. no, linear
101. 104
c. y = 4x + 1
102. 1314
d.
103. 2a9
160
140
120
100
80
60
40
20
0
104. 5x2
105.
a. 1
b. 4
c. 4(1x)
d.
0
1
2
95.
a. 5
b. 4
c. 1280
d. 5 years
3
4
5
160
140
120
100
80
60
40
20
0
0
96.
a. exponential
1
2
3
4
5
1
2
3
4
5
106.
b. 12
a. 1
c. 12(3x)
b. 7
c. 7(1x)
97.
d.
a. linear
b. 50
c. y = 5x + 50
98.
A. exponential, 60(4x)
B. exponential, 12(3x)
C. absolute value, │x-4│
160
140
120
100
80
60
40
20
0
0
D. linear, y = 2.5x-6
E. neither
F. exponential, 64(8x)
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107.
a. 9
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b. none, linear
114. s5
c. y = 28x+250
115. 10446
d.
116. 426
160
140
120
100
80
60
40
20
0
117. 6x25
118.
A-2.4
B-1.8
C-3.5
D-4.7
0
1
2
3
4
5
E-1.2
F-3.9
108.
a. 32
119.
1.25, 1.07, 42%, 150%, 20%, 1.5, 1.42, 43%
b. 8
c. 2048
120.
a. 1.07
d. 5
b. 1125.57
109.
a. exponential
121.
b. 50
a. 1.03
c. 50(3x)
b. 67.20
122.
110.
a. linear
a. 1.05
b. 250
b. 1550.02
c. y=28x+250
123. 100
124. -8
111.
A-linear, y=-3x+12
125. -32
B-exponential, 55(5x)
126. 9
C-neither
127. -27
D-absolute value, │x-7│
128. -1
E-exponential, 10(3x)
129. -10000000
F-exponential, 864(6x)
130. 256
112. z6
131. 1
113. m2
132. -8
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133.
148.
A- 1.7
0
500
B- 2.5
1
333
2
222
3
148
4
99
5
66
6
44
7
29
8
19
C- 4.2
D- 3.4
E- 2.3
F- 1.3
134.
45%, 7%, 1.04, 1.88, 23%, 40%, 1.28, 1.3
135.
a. 1.04
b. 500
b. 1184.34
c. .66
136.
d. 500(2/3)x
a. 1.07
b. 2621.59
149.
a.
137.
a. 1.05
0
700
b. 822.59
1
525
2
394
3
296
4
222
5
167
6
125
7
94
8
71
138. 36
139. -216
140. 81
141. -243
142. -3125
143. -1000000000
144. 1
145. 100000000
146. -6
b. 700
147. -64
c. .75
d. 700(3/4)x
150.
50%, 75%, .70, .55, 10%, 95%, .1, .92
151. x12
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152. y10
162.
153. c6
0
1000
154. 216
1
800
2
640
3
512
4
410
5
328
6
262
7
210
8
168
155. 342
156. 56180
157.
4854
158. w480
159. 1227
160. z30
161.
0
850
1
425
2
213
3
107
4
54
5
27
6
14
7
7
166. x70
8
4
167. 1032
b. 1000
c. .8
d. 1000(4/5)x
163.
97%, 35%, .72, .28, 68%, 52%, .47, .60
164. 1627
165. 1218
b. 850
168. a42
c. .5
169. t72
d. 850(1/2)x
170. r49
171. 36
172. q24
173. 5436
174.
a. 57
b. 1210
c. 33
d. 46
e. 58
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f. 102
d. 15-40
g. 32
e. 68
h. 53
f. 113
i. 9-3
g. 74
j. 12-2
h. 114
k. 105
i. 3-2
l. 27
j. 2-4
k. 134
175.
a. 4m10
b. -4z6
l. 59
177.
c. a8b12
a. -33r3
d. -25x10y15
b. 35y10
e. 24x12
c. -26r30s12
f. -35h15
d. x5y10
g. -43b9
e. –a6b9
h. 55a15
f. -24r8s4
i. 34x8y16
g. 43u3v15
j. –j14
h. c6
k. 1/34
i. –d10
l. 1/(-4)3
j. 45x30y10
m. 1/7
k. 1/42
n. 1/(-3)2
l. 1/(-x)2
o. 11/m5
m. 1/(-5)2
p. 2/a3
n. 1/78
q. 7/s4
o. 5/x4
r. 7t2/s4
p. 1/x7
s. v2/n5
q. 7a/b2
t. 1/52p
r. s2/r4
s. 3/s2
176.
a. 1214
t. y7/x5
b. 210
c. 5-15
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Unit Review
21.
1. C
a. The relationship is exponential because the
previous number is multiplied by 3.4 to receive the next
number
2. B
3. B
b.
4. C
i. 3.4
5. C
ii. 1.034
6. C
iii. 1
7. B
c.
8. A
2000
9. B
1500
10. C
1000
11. B
12. B
500
13. C
0
14. D
0
15. B
d. 3.4x
2
4
16. 4●4=16, 2●2●2●2=16, 4●2=8
17. There is a petri dish full of bacteria. Every day the
bacteria quadruple. In this problem the growth factor is 4
because the previous population is multiplied by four
every day.
18.
0
1
2
3
4
5000
6000
7200
8640
10368
19. y=1286.49
20. exponential
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6
8