Exponential growth: It gets bigger at an increasing rate

1
Exponential growth It gets bigger at an
increasing rate
people who own album
days since album release
2
Writing a rule for exponential growth
Each week twice as many people own the album as
did the day before
3
Turn words into math
Each week twice as many people own the album as
did the day before
Let x be the weeks since release Let y be the
people who own the album Assume that only one
person owned the album to start
4
Name that function
One of these functions is a linear function, and
one is an exponential function. How could you
tell which is which?
5
Linear Functions
ymxb
No exponents
6
Exponential Functions
The variable IS the exponent
yabx
The RATIO of successive y-terms is constant
7
Write a Rule for an Exponential Function
yabx
How can we find out what a and b are?
8
You try
Write a rule for this exponential function
9
Exponential Growth Model
y how much of something you have after t time t
how much time the stuff has been increasing r
rate at which its increasing aamount you
started with
10
Why should we care about this?
Youre saving for college, and you put 1000 in a
bank account today. The account earns 5 annual
interest. How much money will you have when you
go college?
11
Mrs. Devers Old Camaro
If I had kept my 1969 Camaro RS,, what would it
be worth today?
I bought it in 1989 for 10,000 Its value
increases by about 5.5 per year.
If I had done the math at the time, I wouldnt
have sold the car!
12
Exponential decay It gets smaller at a
decreasing rate
people who own a turntable
years since peak LP usage
13
Exponential Decay
yabx
How can we find out what a and b are?
y1(1/4)x
14
Exponential Decay Model
y how much of something you have after t time t
how much time the stuff has been decreasing r
rate at which its decreasing aamount you
started with
15
Using Exponential Decay
Cs-137 has a half life of about 30 years. If you
start with a 5000kg sample, how much of it is
still radioactive after 60 years?
rrate of decay per half life 50 t number of
time periods (half lives)