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.
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. 83 =
b. 56 =
c. 27 =
d. 93 =
e. 144 =
5. Explain how the meanings of 24, 42 and 2 x 4 differ.
6. Find:
a. Five squared
b. Two to the fifth power
c. 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?
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.
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19. 24 =
20. 33 =
21. 92 =
22. 106 =
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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. 35
b. 82
c. 104
d. 123
e. 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 =
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. 10 * 10 * 10 * 10 * 10
36. 6 * 6 * 6
37. n * n
38. y * y * y * y * y
39. 94 * 94 * 94 * 94
Write using exponents.
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40. q squared
41. seven to the fourth
42. three to the fifth
43. five cubed
44. two to the sixth
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Evaluate each expression
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45. 53=
46. 340 =
47. 561=
48. 82 =
49. 63 =
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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=3x2
54. y=4x3
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.
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61. m2 * m5 =
62. c5 * c4 * c2 =
63. y3 * y3 =
64. 5z3 * z5 =
65. 6p8 * 4p3=
66. b2 * b =
67. d4 * d3 * d
68. x3 * x * x5 * x4 =
69. (3xy2)(8xy4) =
70. p3 * q4 * q7 =
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Homework
Write whether the equation shows a linear growth or an exponential growth.
71. y=2x+3
72. y=1.2x2+4
73. y=1.2x+32
74. y=4x+1
75. y=2x3
Does the graph show an exponential growth or a linear growth?
76. ______/ 77. ______/ 78. ______Do the tables show an exponential growth or a linear growth?
79. ______/ 80. ______/ 81. ______Simplify.
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82. v7 * v7 =
83. t * t8 * t10 =
84. –n7 * -6n8 =
85. -10z6 * 3z4 =
86. x2 * x6 =
87. (-5u2v3)(4uv2) =
88. (-3j3k)(-5j2k2) =
89. 54n * -2n3 =
90. a3 * c4 * c3 * a7 =
91. w8 * w7 =
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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 / Y0 / 1
1 / 3
2 / 9
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 / Y0 / 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 / Y0 / 1
1 / 5
2 / 9
3 / 13
4 / 17
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(4t). 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 rabbits0 / 12
1 / 36
2 / 108
3 / 324
4 / 972
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 whales0 / 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.
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Table A
X / y0 / 60
1 / 240
2 / 960
3 / 3840
4 / 15360
Table D
X / y5 / 6.5
6 / 9
7 / 11.5
8 / 14
9 / 16.5
Table B
x / y1 / 12
2 / 36
3 / 108
4 / 324
5 / 972
Table E
x / Y0 / 6
1 / 7
2 / 10
3 / 15
4 / 22
Table C
x / Y1 / 3
2 / 2
3 / 1
4 / 0
5 / 1
Table F
x / Y2 / 64
3 / 512
4 / 4096
5 / 32768
6 / 262144
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Simplify.
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99. a9 ÷ a4 =
100. x21 ÷ x5 =
101. 107103
102. 1321137
103. 10a12÷5a3
104. 20x44x2
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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.
X / Y0 / 1
1 / 4
2 / 16
3 / 64
4 / 256
106. 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 / Y0 / 1
1 / 7
2 / 79
3 / 343
4 / 2401
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 / Y0 / 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(4t). 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?
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. Write an equation to represent the data in the table.
Year / Total rabbits0 / 50
1 / 150
2 / 450
3 / 1350
4 / 4050
110. 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 whales0 / 250
1 / 278
2 / 306
3 / 334
4 / 362
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.
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Table A
X / y0 / 12
1 / 9
2 / 6
3 / 3
4 / 0
Table D
X / y5 / 2
6 / 1
7 / 0
8 / 1
9 / 2
Table B
x / y1 / 55
2 / 275
3 / 1375
4 / 6875
5 / 34375
Table E
x / y0 / 10
1 / 30
2 / 90
3 / 270
4 / 810
Table C
x / y0 / 15
1 / 16
2 / 19
3 / 24
4 / 31
Table F
x / y3 / 864
4 / 5184
5 / 31104
6 / 186624
7 / 1119744
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Simplify
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112. z14z8
113. m20÷m18
114. s20s15
115. 104731027
116. 434÷48
117. 30x375x12
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Growth Factors and Growth Rates
Classwork
118. What is the growth factor in each of the following exponential tables below?
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Table A
X / y0 / 4
1 / 9.6
2 / 23.04
3 / 55.296
4 / 132.71
Table D
X / Y3 / 103.8
4 / 488.0
5 / 2293.5
6 / 10779.2
7 / 50662.3
Table B
x / y1 / 1.8
2 / 3.24
3 / 5.83
4 / 10.50
5 / 18.90
Table E
x / y0 / 13
1 / 15.6
2 / 18.72
3 / 22.46
4 / 26.96
Table C
x / Y2 / 61.25
3 / 214.38
4 / 750.31
5 / 2626.09
6 / 9191.33
Table F
x / Y1 / 31.2
2 / 121.7
3 / 474.6
4 / 1850.8
5 / 7217.9
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