Download 6.1 Exponential Growth and Decay - Ell

6.1
Exponential Growth and Decay
Date: ______________
Warm-Up
Rewrite each percent as a decimal.
1.) 8%
2.) 2.4%
3.) 0.01%
0.08
0.024
0.0001
Evaluate each expression for x = 3.
4.) 2x
5.) 50(3)x
6.) 22x-1
8
1350
32
Exponential Functions
An equation of the form y = a•bx
Examples
y = 2(5)x
y = 0.9(4.2)x
If b > 1, then the function models
exponential growth.
If 0 < b <1, then the function models
exponential decay.
Classify each as exponential growth or
exponential decay.
t
x
1) y  10(1.04)
4) y  12(0.97)
Exponential
Exponential
Growth
Decay
2) y  0.8(1  0.3)
Exponential
Growth
3) y  7(2)
Exponential
Growth
t
x
5) y  15(1  0.6)
Exponential
Decay
6) y  0.5(4)
Exponential
Growth
t
x
A population of 10 hamsters will triple every
year for 4 years. What will be the population
after 4 years?
a = start value
t
y = ab
b = growth factor
t = # of time periods
y  10  3
y  810 hamsters
4
A population of 1000 bacteria will double every
hour. What will be the population after 24 hours?
after 5 days?
a = start value
t
y = ab
b = growth factor
t = # of time periods
y  1000  2
y  16, 777, 216, 000 bacteria
24
y  1000  2
39
y  1.33 10 bacteria
120
Exponential Functions Involving
Percent of Increase
y = a(1 + r)t
a = start value
r = % increase
t = # of time periods
A colony of 10,000 ants can increase by 15%
in a month. How many ants will be in the colony
after 1 year?
12
y  10, 000(1  .15)
y  53,500 ants
A baby weighing 7 pounds at birth may increase
in weight by 11% per month for the first 12 months.
How much will the baby weigh after 1 year?
y  7(1  .11)
12
y  24.5 pounds
1
A deposit of $1500 in an account pays 7 %
4
interest compounded annually. How much
will be in the account after 8 years?
y  1500(1  .0725)
8
y  $2625.85
Exponential Functions Involving
Percent of Decrease
y = a(1 − r)
a = start value
r = % decrease
t = # of time periods
t
A radioactive material decays at 10% per year.
How much of the 12 pound material will be left
after 20 years?
y  12(1  .10)
y  1.46 lbs.
20
Find the value of a downtown office building that
cost 12 million dollars to build 20 years ago and
depreciated at 9% per year.
y  12(1  .09)
y  12(.91)
20
20
y  1.82 Million Dollars