1. Review: exponential growth and Decay functions

2. In this lesson, you will review how to write an exponential growth and decay function modeling a percent of increase situation or decrease situation by interpreting the percent of increase as a growth factor or percent of decrease as a decay factor.

3. Review: exponential growth functions Exponential growth happens by repeated multiplication by the same number.

4. Review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

5. Review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

6. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

7. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

8. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

9. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

10. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

11. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory.

12. review: exponential growth functions

13. A certain species of bacteria will double in population each week in a laboratory.

14. Review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. The growth factor is 2.

15. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria.

16. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria.

17. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria.

18. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria.

19. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria.

20. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria.

21. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. The initial value is 25.

22. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria.

23. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began

24. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity

25. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity

26. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity

27. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity growth factor initial value

28. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity growth factor initial value

29. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity initial value 2

30. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity initial value 2

31. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity 2 25

32. review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. Suppose you initially have 25 specimens of this bacteria. Let x = number of time periods since growth began Let y = amount of the growing quantity

40. interpreting a percent of increase as a growth factor

41. The amount of money in your savings account increased by 3% last year.

42. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

43. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

44. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

45. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

46. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

47. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

48. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

49. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

50. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

51. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

52. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

53. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

54. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

55. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

56. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

57. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

58. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

59. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

60. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

61. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

62. interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year. What does it mean to grow by 3%?

63. an example

64. A certain savings account pays 2% interest per year. You open one of these accounts and put $300 into the account. Assume you do not take out or put in any money from the account after the initial $300. Write a two- variable equation modeling the situation. Be sure to define the variables.

65. an example A certain savings account pays 2% interest per year. You open one of these accounts and put $300 into the account. Assume you do not take out or put in any money from the account after the initial $300. Write a two- variable equation modeling the situation. Be sure to define the variables.

66. an example A certain savings account pays 2% interest per year. You open one of these accounts and put $300 into the account. Assume you do not take out or put in any money from the account after the initial $300. Write a two- variable equation modeling the situation. Be sure to define the variables.

67. an example A certain savings account pays 2% interest per year. You open one of these accounts and put $300 into the account. Assume you do not take out or put in any money from the account after the initial $300. Write a two- variable equation modeling the situation. Be sure to define the variables.

68. an example A certain savings account pays 2% interest per year. You open one of these accounts and put $300 into the account. Assume you do not take out or put in any money from the account after the initial $300. Write a two- variable equation modeling the situation. Be sure to define the variables.

69. In this lesson, you will learn to write an exponential decay function modeling a percent of decrease situation by interpreting the percent of decrease as a decay factor.

70. Review: exponential growth and exponential decay

72. If the change factor is greater than 1: Review: exponential growth and exponential decay

73. If the change factor is greater than 1: exponential growth Review: exponential growth and exponential decay

74. If the change factor is greater than 1: exponential growth (growth factor) Review: exponential growth and exponential decay

75. If the change factor is greater than 1: If the change factor is between 0 and 1: exponential growth (growth factor) Review: exponential growth and exponential decay

76. If the change factor is greater than 1: If the change factor is between 0 and 1: exponential growth (growth factor) exponential decay Review: exponential growth and exponential decay

77. If the change factor is greater than 1: If the change factor is between 0 and 1: exponential growth (growth factor) exponential decay (decay factor) Review: exponential growth and exponential decay

78. growth factor (greater than 1) decay factor (less than 1) Review: exponential growth and exponential decay

79. growth factor (greater than 1) decay factor (less than 1) Example: 2 review: exponential growth and exponential decay

80. growth factor (greater than 1) decay factor (less than 1) Example: 2 Review: exponential growth and exponential decay

81. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

82. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

83. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

84. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

85. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

86. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

87. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

88. growth factor (greater than 1) decay factor (less than 1) Example: 2becomes Review: exponential growth and exponential decay

89. percent of decrease as a decay factor

90. The population of a country decreases by 3%.

91. percent of decrease as a decay factor The population of a country decreases by 3%.

92. percent of decrease as a decay factor The population of a country decreases by 3%.

93. percent of decrease as a decay factor The population of a country decreases by 3%.

94. percent of decrease as a decay factor The population of a country decreases by 3%.

95. percent of decrease as a decay factor The population of a country decreases by 3%.

96. percent of decrease as a decay factor The population of a country decreases by 3%.

97. percent of decrease as a decay factor The population of a country decreases by 3%.

98. percent of decrease as a decay factor The population of a country decreases by 3%.

99. percent of decrease as a decay factor The population of a country decreases by 3%.

100. percent of decrease as a decay factor The population of a country decreases by 3%.

101. percent of decrease as a decay factor The population of a country decreases by 3%.

102. percent of decrease as a decay factor The population of a country decreases by 3%.

103. percent of decrease as a decay factor The population of a country decreases by 3%.

104. percent of decrease as a decay factor The population of a country decreases by 3%. becomes

105. percent of decrease as a decay factor The population of a country decreases by 3%. The decay factor is 0.97! becomes

106. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

107. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

108. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

109. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

110. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

111. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

112. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

113. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation. becomes

114. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation. becomes

115. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation. becomes

116. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

117. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

118. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

119. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

120. an example The value of a car depreciates 15% per year after it is purchased. The value of the car at the time of its purchase was $20,000. Write a two-variable equation to model this situation.

121. Now you know how to write an exponential decay function modeling a percent of decrease situation!