8.1 Exploring Exponential Models
Few things are impossible to diligence and skill. Great
works are performed not by strength, but perseverance.
Exponential Equations
An exponential function is a function with the general form y  ab x,
where x is a real number, a  0 , b  0 , and b  1 .
When b  1 , b is the growth factor and you can use the exponential
function to model growth.
Ex1) Graph:
x
y2
x
-3
-2
-1
0
1
2
3
2x
2-3
2-2
2-1
20
21
22
23
y
Step 2: plot points
and connect
9
8
7
6
5
4
3
2
1
-5 -4 -3 -2 -1
1
-1
2
3
4
5
Application Example
If you know the rate of increase r, then the growth factor b = 1 + r.
Ex2) The population of the United States in 1994 was almost 260 million
with an average annual rate of increase of about 0.7%.
a. Find the growth factor for that year.
b. Suppose the rate of growth had continued to be 0.7%. Write a
function to model this population growth.
c. Predict U.S. population in 2015 to the nearest million.
Additional Example ~ You Try…
Ex3) Write an exponential function y = abx for a graph that
includes (2, 4) and (3, 16).
Graphing Exponential Decay
When b  1, b is the decay factor and you can use the exponential
function to model decay.
Ex4) Graph y = 36(0.5)x. Identify the horizontal asymptote.
Step 1: Make a table of values.
x
–3
–2
–1
0
1
y
Step 2: Plot points and connect
An asymptote is a line that
a graph approaches as x or y
increases in absolute value.
2
3
Exponential Equations
Ex 5) Determine whether each function represents exponential growth or
decay.
x
1


y  16 
y  1000.12x
y  0.25x
 2
What is the
percent of
increase or
decrease?
Ex 6) For each annual rate of change, find the corresponding growth or
decay factor.
 80%
 15.5%
 2.25%
Application Example
Ex7) Suppose you buy a used car that costs $11,800. After
one year the value of the car is $9,440. Estimate the
depreciated value of the car after 6 years.
8.1 Exploring Exponential Models
HW: 1, 7-27 odd, 35-41 all, 46-53 all
Few things are impossible to diligence and skill. Great
works are performed not by strength, but perseverance.
Exponential Equations
Ex 4) Determine whether each function represents exponential
growth or decay.
x
1
 
x
y

16
y  1000.12x
 
y  0.25
 2
What is the
percent of
increase or
decrease?
Ex 5) For each annual rate of change, find the corresponding growth
or decay factor.
 80%
 15.5%
 2.25%