Date WarmUp Rewrite each percent as a decimal 1 8 2 24 3 001 008 0024 00001 Evaluate each expression for x 3 4 2 x 5 503 x 6 2 ID: 628733
Download Presentation The PPT/PDF document "6.1 Exponential Growth and Decay" is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
Slide1
6.1Exponential Growth and Decay
Date: ______________Slide2
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 32Slide3
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.Slide4
Classify each as exponential growth or
exponential decay.
1)
2)
3)
4)
5)
6)
Exponential
Growth
Exponential
Growth
Exponential
Growth
Exponential
Decay
Exponential
Decay
Exponential
GrowthSlide5
A population of 10 hamsters will triple every
year for 4 years. What will be the population
after 4 years?
y = ab
t
b = growth factor
a = start value
t = # of time periodsSlide6
A population of 1000 bacteria will double every
hour. What will be the population after 24 hours?
after 5 days?
y = ab
t
b = growth factor
a = start value
t = # of time periodsSlide7
Exponential Functions Involving
Percent of Increase
A colony of 10,000 ants can increase by 15%
in a month. How many ants will be in the colony
after 1 year?
y = a(1 + r)
t
r = % increase
a = start value
t = # of time periodsSlide8
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? Slide9
A deposit of $1500 in an account pays
interest compounded annually. How much
will be in the account after 8 years? Slide10
A radioactive material decays at 10% per year.
How much of the 12 pound material will be left
after 20 years?
y = a(1 − r)
t
r = % decrease
a = start value
t = # of time periods
Exponential Functions Involving Percent of Decrease Slide11
Find the value of a downtown office building that
cost 12 million dollars to build 20 years ago and
depreciated at 9% per year.