Transcript 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?

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.
Growth factor?
b = 100% + 1% = 101% = 1.01
Exponential Equation: y = abx
y = (130000)(1.01)x
y=
x
(130000)(1.01)
Find population size in 7 years!
x=7
y = (130000)(1.01)7
y = 139377.5958
Or approximately 139,000
A population of 3,000,000 decreases by
1.5% each year.
Initial value? a = 3000000
Growth or decay? Decay!
b will between 0 and 1.
Decay factor?
b = 100% - 1.5% = 98.5% = .985
Exponential Equation: y = abx
y = (3000000)(.985)x
y=
x
(3000000)(.985)
Find population size in 5 years!
x=5
y = (3000000)(.985)5
y = 2,781,649.507
Or approximately 2.78 million
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.
Decay factor?
b = 100% - 20% = 80% = .80
Exponential Equation: y = abx
y = (900)(.80)x
y=
x
(900)(.80)
Find value in 6 years!
x=6
y = (900)(.80)6
y = 235.9296
Or $235.93
An investment of $3,000 earns 4%
interest compounded annually.
Initial value?
a = 3000
Growth or decay? Growth!
b will be greater than 1.
Growth factor?
b = 100% + 4% = 104% = 1.04
Exponential Equation: y = abx
y = (3000)(1.04)x
y=
x
(3000)(1.04)
Find population size in 8 years!
x=8
y = (3000)(1.04)8
y = 4105.707151
Or $4105.71