1. In this lesson, you will learn to write an exponential growth function modeling a percent of increase situation by interpreting the percent of increase as a growth factor.

2. review: exponential growth functions

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.
(𝟎 𝐰𝐞𝐞𝐤𝐬, 𝟏 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

7. review: exponential growth functions
A certain species of bacteria will double in population each week in a laboratory.
(𝟏 𝐰𝐞𝐞𝐤𝐬, 𝟐 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

8. review: exponential growth functions
A certain species of bacteria will double in population each week in a laboratory.
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟒 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

9. review: exponential growth functions
A certain species of bacteria will double in population each week in a laboratory.
(𝟑 𝐰𝐞𝐞𝐤𝐬, 𝟖 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

10. review: exponential growth functions
A certain species of bacteria will double in population each week in a laboratory.
(𝟒 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟔 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

11. review: exponential growth functions
A certain species of bacteria will double in population each week in a laboratory.
(𝟓 𝐰𝐞𝐞𝐤𝐬, 𝟑𝟐 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

12. review: exponential growth functions
A certain species of bacteria will double in population each week in a laboratory.
(𝟔 𝐰𝐞𝐞𝐤𝐬, 𝟔𝟒 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

13. review: exponential growth functions
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.
(𝟎 𝐰𝐞𝐞𝐤𝐬, 𝟐𝟓 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.
(𝟏 𝐰𝐞𝐞𝐤𝐬, 𝟓𝟎 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.
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟎𝟎 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.
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟎𝟎 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.
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟎𝟎 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

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. 𝑥 𝑦
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟎𝟎 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 𝒙 𝑦
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟎𝟎 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

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 𝑥 𝒚
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟎𝟎 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

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 𝑥 𝑦
(𝟐 𝐰𝐞𝐞𝐤𝐬, 𝟏𝟎𝟎 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

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
(𝟐, 𝟏𝟎𝟎)

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
𝒚=( ) ( ) 𝒙
initial value
growth factor
(𝟐, 𝟏𝟎𝟎)

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
𝒚=( ) ( ) 𝒙
initial value
growth factor
(𝟐, 𝟏𝟎𝟎)

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
𝒚=( ) ( ) 𝒙
initial value 2
(𝟐, 𝟏𝟎𝟎)

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
𝒚=( ) ( ) 𝒙
initial value 2
(𝟐, 𝟏𝟎𝟎)

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
𝒚=( ) ( ) 𝒙 25 2
(𝟐, 𝟏𝟎𝟎)

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
𝒚=(𝟐𝟓) (𝟐) 𝒙
(𝟐, 𝟏𝟎𝟎)

33. 𝒚=(𝟐𝟓) (𝟐) 𝒙
(𝟐, 𝟏𝟎𝟎)

34. 𝒚=(𝟐𝟓) (𝟐) 𝒙
(𝟐, 𝟏𝟎𝟎)

35. 𝒚=(𝟐𝟓) (𝟐) 𝒙
(𝟐, 𝟏𝟎𝟎)

36. 𝒚=(𝟐𝟓) (𝟐) 𝟐
(𝟐, 𝟏𝟎𝟎)

37. 𝒚=(𝟐𝟓) (𝟐) 𝟐
(𝟐, 𝟏𝟎𝟎)

38. 𝒚=(𝟐𝟓) (𝟐) 𝟐
(𝟐, 𝟏𝟎𝟎)

39. 𝒚=(𝟐𝟓) (𝟐) 𝟐
(𝟐, 𝟏𝟎𝟎)

40. interpreting a percent of increase as a growth factor

41. interpreting a percent of increase as a growth factor
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%? 1

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%? 1 2 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%? 1

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%?
3%=0.03 1

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%?
3%=0.03 1

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%?
0.03
3%=0.03

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%?
3%=0.03 1

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%?
3%=0.03 1

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%?
3%=0.03 1

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%?
0.03
3%=0.03 1

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%?
0.03
3%=0.03 1

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%?
0.03
3%=0.03 1

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%?
0.03
3%=0.03 1

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%?
0.03
3%=0.03 1

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%?
3%=0.03 1
0.03

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%?
3%=0.03 1
0.03

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%?
3%=0.03
1+0.03

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%?
3%=0.03
1.03

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%?
3%=0.03
1.03 is the growth factor!

63. an example

64. 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.

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.
Growth factor:

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.
Growth factor: 1.02

69. 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.
Growth factor: 1.02

70. 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.
Growth factor: 1.02
Initial value: 300

71. 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.
Growth factor: 1.02
Initial value: 300

72. 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.
Growth factor: 1.02
Initial value: 300

73. 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.
𝒚=( ) ( ) 𝒙
initial value
growth factor
Growth factor: 1.02
Initial value: 300

74. 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.
𝒚=( ) ( ) 𝒙
initial value
Growth factor: 1.02
Initial value: 300

75. 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.
𝒚=( ) ( ) 𝒙
initial value
Growth factor: 1.02
Initial value: 300

76. 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.
𝒚=( ) ( ) 𝒙
Growth factor: 1.02
Initial value: 300

77. 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.
𝒚=( ) ( ) 𝒙
Growth factor: 1.02
Initial value: 300

78. 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.

79. 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.

80. 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.

81. 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.

82. 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.

83. 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.

84. Now you know how to write an exponential growth function modeling a percent of increase situation!