Exponential Growth vs. Decay
hx = 0.5x
8
6
f  x = 2 x
6
4
4
2
2
-5
-2
Exponential Growth
y = a∙bx
b>1
-5
5
Exponential Decay
y = a∙bx
0<b<1
Exponential Growth and Decay Models
y = (1 +
x
)
r is positive for growth
r is negative for decay
Growth or decay? What percentage?
1. y = 67(1.06)x
2. y = -98(.87)x
3. y = 300(1.27)x
4. y = 142(.35)x
5. y = 5(2)x
Example 1: iPads
y = (1 + )x
The value of an iPad decreases at 35% per year. If the
starting price of the iPad is $500, write the exponential
function.
How much will the iPad be worth after 5 years?
When can you buy the iPad for $5?
Example 2: Forest
y = (1 + )x
Suppose the acreage of forest is decreasing by 2% per
year because of development.
If there are currently 4,500,000 acres of forest, how much
forest land will there be in 6 years?
Example 3: Investing
y = (1 + )x
Find a bank account balance to the nearest dollar, if the
account starts with $100, has an annual rate of 4%, and
the money is left in the account for 12 years.
If you wanted to buy a new gaming system for $250,
when will you have enough?
Example 4: Car Salesman
y = (1 + )x
Dave bought a car 8 years ago for $5400. To buy
a similar car today would cost $12,500.
Assuming a steady rate of increase, what was
the yearly rate of inflation?
Half Life
• Some unstable substances,
like plutonium, decay over
time. To measure the rate of
decay, scientists refer to their
“half life.”
• The half life is the time it
takes for half the initial
amount of the substance to
decay.
Example 5: DDT
y = (1 + )x
The pesticide DDT was widely used in the United States
until its ban in 1972. Write an equation that models
the 15 year half-life of 100 grams of DDT.
How much DDT would be remaining after 45 years?
Example 6:
228Ac
y = (1 + )x
228Ac
has a half life of 6.13 hours. Write an equation that
models the half life of a 5 mg sample.
How much 228Ac would be remaining after one day?