Exponential Functions

Exponential Growth

Exponential Decay

Created by:David W. Cummins

A population of 130,000 increases by 1% each year.

Initial value? a = 130000

Growth or decay? Growth!b will be greater than 1.

b = 100% + 1% = 101% = 1.01Growth factor?

Exponential Equation: y = abx

y = (130000)(1.01)x

Find population size in 7 years!

x = 7y = (130000)(1.01)7

y = 139377.5958

Or approximately 139,000

y = (130000)(1.01)x

A population of 3,000,000 decreases by 1.5% each year.

Initial value? a = 3000000Growth or decay? Decay!

b will between 0 and 1.

b = 100% - 1.5% = 98.5% = .985Decay factor?

Exponential Equation: y = abx

y = (3000000)(.985)x

Find population size in 5 years!x = 5

y = (3000000)(.985)5

y = 2,781,649.507

Or approximately 2.78 million

y = (3000000)(.985)x

An item purchased for $900 has a 20% loss in value each year.

Initial value? a = 900

Growth or decay?Decay!b will between 0 and 1.

b = 100% - 20% = 80% = .80Decay factor?

Exponential Equation: y = abx

y = (900)(.80)x

Find value in 6 years!x = 6

y = (900)(.80)6

y = 235.9296

Or $235.93

y = (900)(.80)x

An investment of $3,000 earns 4% interest compounded annually.

Initial value?a = 3000Growth or decay? Growth!

b will be greater than 1.

b = 100% + 4% = 104% = 1.04Growth factor?

Exponential Equation: y = abx

y = (3000)(1.04)x

Find population size in 8 years!x = 8

y = (3000)(1.04)8

y = 4105.707151

Or $4105.71

y = (3000)(1.04)x