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Rhonda hears a rumor at 8:00 A.M. She
immediately tells her two best friends the rumor.
One hour later Rhonda’s friends have each told
two of their friends. This pattern continues each
hour, with each friend reporting the rumor to two
friends who have not already heard it. By 8:00
P.M. that evening, how many people have heard
the rumor?
Answer: 8191
Chapter 8 Section 1
Exponential Growth
Mr. Ochoa
Algebra II
Vocabulary
•
•
•
•
Exponential FunctionBaseAsymptoteExponential Growth
Function• Growth Factor-
Objective - To graph exponential functions
and to model them in real-life situations.
Examples
y  12(5)
x
y  0.2(3.8)
Exponential Growth Function
An equation of the form y  a b .
With a  0, b  0.
x
x
Graph y  3
x y
2 1 / 9
1 1 / 3
0 1
1 3
2 9
3 27
4 81
5 243
x
y
x
Graph y  3
x
y
y-intercept = 1
asymptote = x-axis
domain: all real numbers
range: y > 0
x
1 x
Graph y  2
4
x y
2 0.0625
1 0.125
0 0.25
1 0.5
2 1
3 2
4 4
5 8
6 16
y
x
1 x
Graph y  2
4
y
y-intercept = 0.25
asymptote = x-axis
domain: all real numbers
range: y > 0
x
Graph y  2 3  1
x
y
x y
2 0.8
1 0.3
0 1
1 5
2 17
3 53
x
Graph y  2 3  1
x
y
y-intercept = 1
asymptote y = -1
domain: all real numbers
range: y > -1
x
Exponential Growth
y  a(1  r)t
a  initial amount
r  % increase
1  r is the growth factor
t  number of time periods
In 2005 the average price of a car was $15,000.
If the price increases 8% a year, what will the
average price be in 10 years?
y  15,000(1  .08)
10
y  $32, 384
Compound Interest
 r
A  P 1  
 n
nt
P  initial principal deposited
r  annual rate
n = compounded times per year
t  years
You deposit $50,000 in an investment account that
pays 6% annual interest. Find the balance after 2
years if the interest is compounded quarterly ?
 r
A  P 1  
 n
nt
P = 50,000, r = 0.06
n = 4, t = 2
 0.06 
A  50, 000 1 

4 

A  $56, 324.63
4 2