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?
Write whether the equation shows a linear growth or an exponential growth.
2. 𝑦 = 2𝑥
3. 𝑦 = 23 + 𝑥
4. 𝑦 = 3𝑥 + 7
5. 𝑦 = 3(2) 𝑥
6. 𝑦 = 4(3) 𝑥
Does the graph show an exponential growth or a linear growth?
7. __________________
8. __________________
9. __________________
Do the tables show an exponential growth or a linear growth?
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10. __________________
11. __________________
12. __________________
Review: Simplify.
13.
14.
15.
16.
17.
m2 * m5 =
c5 * c4 * c2 =
y3 * y3 =
5z3 * z5 =
6p8 * 4p3=
18.
19.
20.
21.
22.
b2 * b =
d4 * d3 * d
x3 * x * x5 * x4 =
(3xy2)(8xy4) =
p3 * q4 * q7 =
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?
Write whether the equation shows a linear growth or an exponential growth.
24. 𝑦 = 2𝑥 + 3
25. 𝑦 = 1.2(2)𝑥 + 4
26. 𝑦 = 1.2𝑥 + 32
27. 𝑦 = 4𝑥 + 1
28. 𝑦 = 2(3) 𝑥
Does the graph show an exponential growth or a linear growth?
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29. __________________
30. __________________
31. __________________
Do the tables show an exponential growth or a linear growth?
32. __________________
33. __________________
x
0
1
2
3
4
5
6
7
y
1.5
3
6
12
24
48
96
192
34. __________________
x
0
1
2
3
4
5
6
7
y
0.2
0.6
1.8
5.4
16.2
48.6
145.8
437.4
Review: Simplify.
35.
36.
37.
38.
39.
v7 * v7 =
t * t8 * t10 =
–n7 * -6n8 =
-10z6 * 3z4 =
x2 * x6 =
40.
41.
42.
43.
44.
(-5u2v3)(4uv2) =
(-3j3k)(-5j2k2) =
54n * -2n3 =
a3 * c4 * c3 * a7 =
w8 * w7 =
Exponential Relationships in Tables, Equations and Graphs
Classwork
45. 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.
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x
Y
0
1
1
3
2
9
3
27
4
81
46. 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
47. 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
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4
17
48. 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?
49. 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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50. 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
51. 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
9
16.5
3
15
4
22
X
y
0
60
x
y
1
240
1
12
x
Y
2
960
2
36
1
3
3
3840
3
108
2
2
4
15360
4
324
3
1
5
972
4
0
5
1
Table B
Table D
Table C
X
y
5
6.5
x
Y
6
9
0
6
x
Y
7
11.5
1
7
2
64
8
14
2
10
3
512
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Table E
Table F
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4
4096
5
32768
6
262144
Simplify.
52. a9 ÷ a4 =
55.
53. x21 ÷ x5 =
54.
1321
137
56. 10𝑎12 ÷ 5𝑎3
107
103
57.
20𝑥 4
4𝑥 2
Homework
58. 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
4
2
16
3
64
4
256
59. 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
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3
343
4
2401
60. 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
61. 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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62. 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
50
1
150
2
450
3
1350
4
4050
63. 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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64. 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
65.
𝑧 14
𝑧8
66. 𝑚20 ÷ 𝑚18
67.
68.
69.
𝑠 20
𝑠 15
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70.
10473
1027
434 ÷ 48
30𝑥 37
5𝑥 12
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Growth Factors and Growth Rates
Classwork
71. 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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72. 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
73. 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?
74. 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?
75. 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?
76. A different fish species triples in population annually.
a. If the fish population starts at 35 fish, create a table that shows the growth over time.
Year
0
1
2
3
4
Fish
35
Population
b. What is the growth factor and y-intercept for this relationship?
5
c. What is the equation that represents this relationship?
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6
Evaluate.
77. (-10)2=
82. (−1)5 =
78. (−2)3 =
83. (−10)7 =
79. (−2)5 =
84. (−4)4 =
80. (−3)2 =
85. (−7)0 =
81. (−3)3 =
86. (−8)1 =
Homework
87. What is the growth factor in each of the following exponential tables below?
Table A
Table C
Table E
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
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
88. Fill in the table below with the missing growth factors and growth rates.
Growth factor
Growth rate
1.50
50%
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1.45
1.07
4%
88%
1.23
1.40
28%
30%
89. 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?
90. 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?
91. 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?
92. A population of bacteria doubles every hour.
a. If the bacteria population starts at 2,100, create a table that shows the growth over time.
Hour
0
1
2
3
4
5
Bacteria
2,100
Population
b. What is the growth factor and y-intercept for this relationship?
c. What is the equation that represents this relationship?
Evaluate.
93. (−6)2 =
98. (−10)9 =
94. (−6)3 =
99. (−7)0 =
95. (−3)4 =
100. (−10)8 =
96. (−3)5 =
101. (−6)1 =
97. (−5)5 =
102. (−4)3 =
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6
Exponential Decay
Classwork
103. 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?
104. 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?
105. 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.
106. (x4)3=
111. (c3)2=
107. (y2)5=
112. (22)8=
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108. (36)7=
113. (w8)60=
109. (569)20=
114. (123)9=
110. (4318)3=
115. (z5)6=
Homework
116. 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?
117. 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?
118. 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%
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72%
0.32
0.48
53%
40%
Simplify.
119. (163)9=
124. (t9)8=
120. (126)3=
125. (r7)7=
121. (x10)7=
126. (33)2=
122. (104)8=
127. (q8)3=
123. (a6)7=
128. (5412)3=
Exponential VS Linear
Classwork
For problems #129 – 137 determine if the data best fits an exponential or linear model and then write that model.
129. model ________
130. model ________
131. model _________
x
y
t
P
x
K
-6
-15
5
-21
2
36
-5
-13
6
-25
3
108
-4
-11
7
-29
4
324
-3
-9
8
-33
5
972
132. model __________
133. model ________
134. model___________
t
V
x
y
x
P
0
3
0
10
3
3
1
7
1
20
6
1
2
11
2
40
9
-1
3
15
3
80
12
-3
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135. model __________
136. model ________
137. model __________
t
N
x
A
t
B
2
25
3
162
1
30
3
125
4
486
2
60
4
625
5
1,458
3
120
5
3,125
6
4,374
4
240
138. Which model is consistent with this population data?
A. y = 4x + 3
B. y = 3(4𝑥 )
C. y = 4
𝑥
D. y = 3x2
y
x
12
1
48
2
192
3
768
4
3072
139 Which model is consistent with this population data?
A. P = 10(6x)
B. P = 6x + 10
C. P = 11x
D. P = 6x + 10
5
P
x
22
2
34
4
46
6
58
8
70
10
140. Which model is consistent with this data which describes a bacteria’s growth over time?
A. B = 50(25t)
𝑡
B. B = 50(25 )
C. B = 2t + 50
D. B = 50(2t)
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B
t
100
5
200
10
400
15
800
20
1,600
25
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Homework
For problems #141 – 149 determine if the data best fits an exponential or linear model and then write that model
141. model __________
142. model __________
143. model __________
x
y
x
R
x
B
3
343
1
-10
1
36
4
2401
2
30
2
144
5
16,807
3
70
3
576
6
117,649
4
110
4
2,304
144. model __________
145. model __________
146. model __________
t
P
x
N
n
C
2
140
2
11
0
5
3
280
4
17
1
15
4
560
6
23
2
45
5
1,120
8
29
3
135
147. model __________
148. model __________
p
K
w
L
0
20
3
-12
1
15
4
-6
2
10
5
0
3
5
6
6
150. Which model is consistent with this population data?
A. P = 9x
2
B. P = 5x + 9
P
x
23
2
41
4
59
6
77
8
95
10
x
C. P = 5(9 )
D. P = 9x + 5
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149. model __________
x
y
3
750
4
3,750
5
18,750
6
93,750
151. Which model is consistent with revenue data?
A. R = 3.50x + 200
B. R = 200x + 3.50
C. R = 200(3.50x)
D. R = 3.50x2 + 200
R
x
203.50
1
207
2
210.50
3
214
4
217.50
5
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152. Which model is consistent with this data which describes a bacteria’s growth over time?
A. G = 45(25t)
𝑡
B. G = 45(25 )
C. G = 5t + 45
D. G = 45(2t)
G
t
1,440
1
46,080
2
1,474,560
3
47,185,920
4
1,509,949,440
5
Writing and Solving Model Equations
Classwork
153. Megan and Audra are trying to raise money for math club activities. They decide to sell T-shirts and on day 1 they
sell $45 worth of T-shirts and on day 4 they sell $121 worth of T-shirts.
Part A
Based on the data Audra thinks the amount of money, m on day, d can be modeled by a linear function. What is the
amount of money predicted by the model on day 10 by a linear model?
Part B
Megan does not agree with Audra and instead believes the data can be modeled by an exponential function.
Compare the two models for 3 days and 7 days.
Part C
Suppose the data can be modeled by a linear function. How much money would they make after 12 days?
154. Mark and Fiona are planning to buy a house and decide to open up a joint savings account. In 2004 there is $5,400
in the account and in 2006 there is $6,067.44 in the savings account.
Part A
Fiona thinks the data can be modeled by exponential function where t is the number of years since 2004 and a is the
amount of money in the account. How much money is in the bank account in 2008?
Part B
Mark thinks the data can be modeled by a linear function. Compare the two models for 2010 and 2012.
Part C
Suppose the data can be modeled by an exponential function. How much money will be in the bank account in 2016?
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155. The population of a town in 1990 was 34,000 people. By 2010 the population of the town had grown to 36,000
people.
Part A
Assume that the population of the town has grown linearly since 1990 and will continue to grow this way. What is the
population of the town in 2024?
Part B
Suppose instead that the population of the town has grown exponentially since 1990. Write an expression for the
population in terms of time t since 1990.
Part C
Suppose that the population is growing exponentially. What will the population of the town be in 2001?
Part D
Another town’s population can be modeled by the function P(t) = 2500(1.35 t/10), where P represents the population
after t years since 1990. Based on the model the population of the town increases by what percent each year?
156. Scientists are exploring the decay rate of certain type of cells. At the beginning of the experiment, there are 2,400
cells. After 2 hours there are 2,050 cells.
Part A
Based on the data Marci believes the data can be modeled by a linear function. Use the function to predict the
number of cells after 5 hours.
Part B
Jordan believes the data can be modeled by an exponential function. Compare the two models for 4 hours and 7
hours.
Homework
157. Olivia and Cecile want to share an apartment when they go to college. They open up a joint savings account and
they notice in month 2 there is $150 and in month 5 there is $300.
Part A
Cecile believes the data can be modeled by a linear function. How much money would be in the account after 10
months?
Part B
Olivia believes the data can be modeled by an exponential function. Compare the models for month 4 and month 7.
Part C
Suppose the data can be modeled by a linear function. How much money will be in the account after one year?
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158. The population of a town in 2005 was 23,400 people. By 2010 the population of the town had decreased to 19,000
people.
Part A
Assume that the population of the town has decreased linearly since 2005 and will continue to decrease this way.
What is the population of the town in 2014?
Part B
Suppose instead that the population of the town has grown exponentially since 2005. Write an expression for the
population in terms of time t since 2005.
Part C
Suppose that the population is growing exponentially. What will the population of the town be in 2016?
Part D
Another town’s population can be modeled by the function P(t) = 35000(0.95t/10), where P represents the population
after t years since 2005. Based on the model the population of the town decreases by what percent each year?
159. Nathan and Connor are studying a population of rabbits. On month 3 they count 36 rabbits and on month 6 they
count 48 rabbits.
Part A
Based on the data, Connor thinks the population of rabbits, p on month, m can be modeled by a linear function. What
is the number of rabbits predicted by the model on month 7 by a linear model?
Part B
Nathan does not agree with Connor and instead believes the data can be modeled by an exponential function.
Compare the two models for 4 months and 8 months.
Part C
Suppose the data can be modeled by a linear function. How many rabbits would they have after 12 months?
160. Scientists are exploring the decay rate of certain type of cells. At the beginning of the experiment, there are 4,600
cells. After 3 hours there are 3,950 cells.
Part A
Based on the data Janis believes the data can be modeled by a linear function. Use the function to predict the number
of cells after 7 hours.
Part B
Max believes the data can be modeled by an exponential function. Compare the two models for 5 hours and 8 hours.
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Unit Review
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.
growth factor
b. starting value
d. growth rate
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.
b. 1
d. 11
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10
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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.
16%
b. 60%
d. 160%
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.
1
128
c.
b.
1
14
1
64
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The table
1
d.
12
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.
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
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
22. Determine if the data best fits an exponential or linear model and then write that model.
a. model _________
b. model _________
x
y
x
y
2
13
1
20
3
16
2
80
4
19
3
320
5
22
4
1,280
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23. The population of a town in 2002 was 15,000 people. By 2006 the population of the town had grown to 22,000 people.
Part A
Assume that the population of the town has grown linearly since 2002 and will continue to grow this way. What is the
population of the town in 2016?
Part B
Suppose instead that the population of the town has grown exponentially since 2002. Write an expression for the
population in terms of time t since 2002.
Part C
Suppose that the population is growing exponentially. What will the population of the town be in 2010?
Part D
Another town’s population can be modeled by the function P(t) = 1800(1.25 t/10), where P represents the population
after t years since 2002. Based on the model the population of the town increases by what percent each year?
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Algebraic Exponents & Exponential Functions Chapter Problems Answer Key
Classwork
14. 2c10
1
15. y6
16. 5z8
a.
1
4
17. 24p11
2
16
18. b3
3
64
19. d8
4
256
5
1024
20. x13
21. 24x2y6
22. p3q11
b. 1048576
23.
c.
a.
number
of cuts
fourths
halves
1
4
2
2
16
3
thirds
1
5
3
2
25
4
9
3
125
64
8
27
4
625
4
256
16
81
5
3125
5
1024
32
243
b. 9765625
c.
Number
of Cuts
Fifths
Halves
Thirds
Fourths
1
5
2
3
4
2
25
4
9
16
3
125
8
27
64
7. linear
4
625
16
81
256
8. exponential
5
3125
32
243
1024
2. linear
3. linear
4. linear
5. exponential
6. exponential
9. exponential
10. linear
24. linear
11. exponential
25. exponential
12. linear
26. linear
13. m7
27. linear
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28. exponential
c. y = 5(1x)
29. exponential
d.
160
140
120
100
80
60
40
20
0
30. linear
31. exponential
32. linear
33. exponential
34. exponential
35. v14
0
36. t19
1
2
3
4
5
2
3
4
5
37. 6n15
38. -30z10
47.
39. x8
a. 1
40. -20u3v5
b. no, linear
41. 15j5k3
c. y = 4x + 1
42. -108n4
d.
160
140
120
100
80
60
40
20
0
43. a10c7
44. w15
45.
a. 1
b. 3
c. y = 3(1x)
0
d.
160
140
120
100
80
60
40
20
0
1
48.
a. 5
b. 4
c. 1280
d. 5 years
49.
0
1
2
3
4
5
a. exponential
46.
b. 12
a. 1
b. 5
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c. 12(3x)
50.
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d.
a. linear
160
140
120
100
80
60
40
20
0
b. 50
c. y = 5x + 50
51.
A. exponential, 60(4x)
B. exponential, 12(3x)
C. absolute value, │x-4│
0
D. linear, y = 2.5x-6
E. neither
1
2
3
4
5
2
3
4
5
60.
F. exponential, 64(8x)
a. 9
52. a5
b. none, linear
53. x16
c. y = 28x+250
54. 104
d.
160
140
120
100
80
60
40
20
0
55. 1314
56. 2a9
57. 5x2
58.
a. 1
b. 4
0
c. 4(1x)
d.
1
61.
160
140
120
100
80
60
40
20
0
a. 32
b. 8
c. 2048
d. 5
62.
a. exponential
0
1
2
3
4
5
b. 50
59.
c. 50(3x)
a. 1
63.
b. 7
a. linear
c. 7(1x)
b. 250
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c. y=28x+250
64.
A-linear, y=-3x+12
76.
a.
Year
Fish
Pop
0
1
2
3
4
5
6
35
105
315
945
2,835
8,505
25,515
B-exponential, 55(5x)
b. GF = 3, Y-int = 35
C-neither
c. P = 35(3t)
D-absolute value, │x-7│
77.100
E-exponential, 10(3x)
78. -8
F-exponential, 864(6x)
79. -32
65. z6
80. 9
66. m2
81. -27
67. s5
82. -1
68. 10446
83. -10000000
69. 426
84. 256
70. 6x25
85. 1
71.
86. -8
A-2.4
87.
B-1.8
A- 1.7
C-3.5
B- 2.5
D-4.7
C- 4.2
E-1.2
D- 3.4
F-3.9
E- 2.3
F- 1.3
72.
1.25, 1.07, 42%, 150%, 20%, 1.5, 1.42, 43%
88.
45%, 7%, 1.04, 1.88, 23%, 40%, 1.28, 1.3
73.
a. 1.07
89.
a. 1.04
b. 1125.57
b. 1184.34
74.
a. 1.03
90.
a. 1.07
b. 67.20
b. 2621.59
75.
a. 1.05
b. 1550.02
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91.
a. 1.05
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92.
Ho
ur
BP
b. 822.59
0
700
a.
1
525
4
5
6
2
394
33,6
00
67,2
00
134,4
00
3
296
4
222
5
167
93.36
6
125
94. -216
7
94
8
71
0
1
2
3
2,1 4,20 8,40 16,8
00
0
0
00
b. GF = 2, Y-int = 2100
c. P=2100(2t)
95. 81
96. -243
b. 700
97. -3125
c. .75
98. -1000000000
d. 700(3/4)x
99. 1
105.
100. 100000000
50%, 75%, .70, .55, 10%, 95%, .1, .92
101. -6
106. x12
102. -64
107. y10
103.
108. c6
0
500
1
333
2
222
111. 56180
3
148
112. 4854
4
99
113. w480
5
66
114. 1227
6
44
115. z30
7
29
8
19
b. 500
c. .66
d. 500(2/3)x
104.
109. 216
110. 342
116.
0
850
1
425
2
213
3
107
4
54
a.
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5
27
128. 5436
6
14
129. Linear: y = 2x – 3
7
7
8
4
130. Linear P = -4t – 1
131. Exponential: K = 4(3x)
132. Linear: V = 4t + 3
b. 850
133. Exponential: y = 10(2x)
c. .5
134. Linear: P =
d. 850(1/2)x
−2
3
x+5
135. Exponential: N = 5t
117.
136. Exponential: A = 6(3x)
0
1000
1
800
2
640
3
512
4
410
5
328
142. Linear R = 40x – 50
6
262
143. Exponential: B = 9(4x)
7
210
144. Exponential: P = 35(2t)
8
168
145. Linear: N = 3x + 5
137. Exponential: B = 15(2x)
138. B
139. D
140. B
141. Exponential: y = 7x
b. 1000
146. Exponential: C = 5(3n)
c. .8
147. Linear: K = -5p + 20
d. 1000(4/5)x
148. Linear: L = 6w – 30
149. Exponential y = 6(5x)
118.
97%, 35%, .72, .28, 68%, 52%, .47, .60
150. D
119. 1627
151. A
120. 1218
152. A
121. x70
153. a. m = 25.33d + 19.67, $272.97
122. 1032
b. m = 32.37(1.39)d, The linear model yields $95.66
for 3 days and is greater than the $86.93 the exponential
model yields. The linear model yields $196.98 for 7 days
and is less than the $324.52 the exponential model
yields.
123. a42
124. t72
125. r49
126. 36
c. $323.63
154. a. m = 5400(1.06)t, $6,817.38
127. q24
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b. m = 333.72t + 5,400, For 2010 the linear model
yields $7,402.32 which is less than the $7,660.00 the
exponential model yields. In 2012 the linear model yields
$8,069.76, which is less than the $8,606.78 the
exponential model yields.
c. $10,865,86
155. a. P = 100t + 34,000; 37,400 people
Unit Review
1. C
2. B
3. B
4. C
b. P = 34,000(1.003)t
5. C
c. 35,139 people
6. C
d. 3%
7. B
156. a. C = -175t + 2,400; 1,525 cells
8. A
b. C = 2,400(0.92)t, The linear model for four hours
predicts 1,700 cells which is less than the 1,719 cells the
exponential model predicts. The linear model for 7 hours
predicts 1,175 cells which is less than the 1,339 cells the
exponential model predicts.
9. B
157. a. y = 50x + 50, $550
b. y = 94.48(1.26)x, For 4 months the linear model
predicts $250, which is more than the exponential model
which predicts $238.13. For 7 months the linear model
predicts $400, which is less than the $476.36 the
exponential model predicts.
c. $650
10. C
11. B
12. B
13. C
14. D
15. B
16. 4●4=16, 2●2●2●2=16, 4●2=8
b. y = 23,400(0.96)x
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.
c. 14,935 people
18.
158. a. y = -880x + 23400; 15,480 people
d. 0.5%
159. a. p = 4m + 24; 52 rabbits
b. p = 26.95(1.101)m, The linear model predicts
after 4 months there will be 40 rabbits which is
approximately the same as the exponential model. The
linear model predicts that in 8 months there will be 56
rabbits which is less than the 58 rabbits the exponential
model predicts.
0
1
2
3
4
5000
6000
7200
8640
10368
19. y=1286.49
20. exponential
c. 72 rabbits
160. a. y = -216.67x + 4600; 3,083 cells
b. y = 4600(0.95)x, The linear model predicts after 5
hours there will be 3,517, which is less than the 3,559
cells the exponential model predicted. After 8 hours, the
linear model predicts there will be 2,867 cells, which is
also less than the 3,052 cells the exponential model
predicted.
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21.
a. The relationship is exponential because the
previous number is multiplied by 3.4 to receive the next
number
b.
i. 3.4
ii. 1.034
iii. 1
c.
2000
1500
1000
500
0
0
2
4
6
8
d. 3.4x
22. a. Linear; y = 3x + 7
b. Exponential; y = 5(4)x
23. a. y = 1750t + 15000; 39,500 people
b. y = 15000(1.1005)t
c. 32,271 people
d. 2.3 %
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