6.1 Exponential Growth and Decay - Ell
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Transcript 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.
1) y 10(1.04) x
4) y 12(0.97) t
Exponential
Exponential
Growth
Decay
2) y 0.8(1 0.3) x
Exponential
Growth
5) y 15(1 0.6) x
Exponential
Decay
3) y 7(2) t
Exponential
Growth
6) y 0.5(4) t
Exponential
Growth
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
4
y 810 ham sters
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
24
y 16, 777, 216, 000 bacteria
y 1000 2
120
y 1.33 10
39
bacteria
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)
y $2625.85
8
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 M illion D ollars