Exponential Growth and Decay Review
1.) Complete the following table:
a)
x
-3
-2
-1
H(x) =
5x
x
G(x) =
(0.2)x
-3
-2
-1
0
1
2
3
0
1
2
3
b) Use your graphing calculator to graph both of the functions above.
c) Use the tables and graphs from parts a and b to complete the following
table:
function
base
Growth
or decay
factor
x-int
y-int
Horizontal Increasing
asymptote or
decreasing
H(x) =
5x
G(x) =
(0.2)x
Example 2:
a) Complete the table below
x
-3
-2
-1
0
1
2
3
F(x)=
0.037
x
3
G(x) = -27
x3
H(x)
-9
=3x
b) use your graphing calculator to graph all three of the functions above
on the calculator at the same time.
c) Describe any similarities or differences that you see in the graphs.
Example 3: Determine the growth and decay factors and growth and
decay rates (%s) in the following tables:
Growth factor
Growth rate
1.02
2.9%
2.23
34%
1.0002
Decay factor
Decay rate
23%
0.32
4.7%
0.803
0.52%
4.) The 2000 US Census reports the populations of Bozeman, Montana as
27,509 and Butte, Montana as 32,370. Since the 1990 census,
Bozeman’s population has been increasing at approximately 1.96% per
year. Butte’s population has been decreasing at approximately 0.29% per
year. Assume that the growth and decay rates stay constant.
a) let P represent the population “t” years after 2000. Determine the
exponential functions that model the populations of both cities.
Bozeman:
Butte:
b) Use the population models to predict the populations of both cities in
2005.
Bozeman:
Butte:
Example 4: You have recently purchased a new truck for $20,000, by
arranging financing for the next five years. You are curious to know what
your new truck will be worth when the loan is completely paid off.
a) Assuming that the value depreciates at a constant rate of 15%, write
an equation that represents the value of the truck “V”, “t” years from
now.
b) What is the decay rate in this situation?
c) What is the decay factor?
d) Use the equation from part “a” to estimate the value of your truck 5
years from now (to the nearest dollar).