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.

review: exponential growth functions

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

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

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

review: exponential growth functions A certain species of bacteria will double in population each week in a laboratory. (𝟎 𝐰𝐞𝐞𝐤𝐬, 𝟏 𝐛𝐚𝐜𝐭𝐞𝐫𝐢𝐚)

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

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

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

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

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

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

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

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

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.

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.

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

𝒚=(𝟐𝟓) (𝟐) 𝒙 (𝟐, 𝟏𝟎𝟎)

𝒚=(𝟐𝟓) (𝟐) 𝒙 (𝟐, 𝟏𝟎𝟎)

𝒚=(𝟐𝟓) (𝟐) 𝒙 (𝟐, 𝟏𝟎𝟎)

𝒚=(𝟐𝟓) (𝟐) 𝟐 (𝟐, 𝟏𝟎𝟎)

𝒚=(𝟐𝟓) (𝟐) 𝟐 (𝟐, 𝟏𝟎𝟎)

𝒚=(𝟐𝟓) (𝟐) 𝟐 (𝟐, 𝟏𝟎𝟎)

𝒚=(𝟐𝟓) (𝟐) 𝟐 (𝟐, 𝟏𝟎𝟎)

interpreting a percent of increase as a growth factor

interpreting a percent of increase as a growth factor The amount of money in your savings account increased by 3% last year.

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%?

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%?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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!

an example

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.

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.

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.

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+0.02

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

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

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

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

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

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

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

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

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

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

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.

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.

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.

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.

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.

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.

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