Growth FactorGrowth Factor

The base number in an exponential The base number in an exponential relationship.relationship.

The constant factor that each value The constant factor that each value is multiplied by to get the next value.is multiplied by to get the next value.• Example: Example:

A = 25(3A = 25(3xx)) The growth factor is 3The growth factor is 3

How to find the Growth Factor from How to find the Growth Factor from a tablea table

Divide a y-value by the previous y-value.Divide a y-value by the previous y-value.• Example:Example:

XX yy

11 100100

22 300300

33 900900

300 divided by 100 = 3

900 divided by 300 = 3

The growth factor is 3

Growth RateGrowth Rate

The percent increase in an exponential The percent increase in an exponential relationship.relationship.• Example: The number of rabbits increased Example: The number of rabbits increased

from 100 to 180, an 80% increase.from 100 to 180, an 80% increase. The growth rate is 80%The growth rate is 80% Written as a decimal, this is .80Written as a decimal, this is .80

Interest is a growth rateInterest is a growth rate

How do I find growth rate if I know How do I find growth rate if I know the growth factor?the growth factor?

Subtract 1 from the growth factor to Subtract 1 from the growth factor to get the growth rate.get the growth rate.• Example: If the growth factor is 1.2, the Example: If the growth factor is 1.2, the

growth rate is 1.2 – 1 = .2 or 20%.growth rate is 1.2 – 1 = .2 or 20%.

How do I find the growth factor if I How do I find the growth factor if I know the growth rate?know the growth rate?

Add 1 to the growth rate.Add 1 to the growth rate.• Example: If the growth rate is 70% (.70) Example: If the growth rate is 70% (.70)

add a 1 to the front of that.add a 1 to the front of that. The growth factor is 1.7.The growth factor is 1.7.

What do I do with a growth factor or What do I do with a growth factor or growth rate?growth rate?

If you have an initial value (If you have an initial value (y-intercepty-intercept), ), knowing the growth factor or growth rate knowing the growth factor or growth rate will help you find subsequent values.will help you find subsequent values.• Example: I have $500 in the bank. If I earn 5% Example: I have $500 in the bank. If I earn 5%

interest for 5 years interest for 5 years (compound growth(compound growth), how ), how much will I have at the end of 5 years?much will I have at the end of 5 years?

Example:Example:Initial value Initial value

at at beginning beginning

of yearof year

Growth Growth rate value rate value

(5%)(5%)

Value with Value with growth growth factor factor (1.05)(1.05)

$500$500 $25$25 $525$525

$525$525 $26.25$26.25 $551.25$551.25

$551.25$551.25 $27.56$27.56 $578.81$578.81

$578.81$578.81 $28.94$28.94 $607.75$607.75

$607.75$607.75 $30.39$30.39 $638.14$638.14

PracticePractice

What is the growth factor for a yearly What is the growth factor for a yearly increase of 7%?increase of 7%?• 1.071.07

What is the growth factor for a yearly What is the growth factor for a yearly increase of 40%?increase of 40%?• 1.4 1.4

PracticePractice

What is the growth rate associated What is the growth rate associated with the growth factor of 1.3?with the growth factor of 1.3?• 30%30%

What is the growth rate of an What is the growth rate of an investment with a growth factor of investment with a growth factor of 1.08?1.08?• 8%8%