8­1 Exploring Exponential Models 2011
April 13, 2011
8­1 Exploring Exponential Models
Objective: Model exponential growth and decay.
1
8­1 Exploring Exponential Models 2011
April 13, 2011
Check Skills You'll Need
2
8­1 Exploring Exponential Models 2011
April 13, 2011
An exponential function is a function
with the general form y = abx, where x is a real number, a ≠0, b > 0, and b ≠ 1.
You can use an exponential function
with b > 1 to model growth. When b > 1, b is the growth factor.
3
8­1 Exploring Exponential Models 2011
April 13, 2011
d
in
iti
al
r
e
t
af
t
s
n
d
u
o
o
i
am per
x
va
e
lu
e
y = ab
x
tim
o
i
r
pe
y
a
c
e
d
r
o
h tor
t
ow fac
r
g
4
8­1 Exploring Exponential Models 2011
April 13, 2011
Graph y = 2x.
5
8­1 Exploring Exponential Models 2011
April 13, 2011
n
o
ti
c
n
u . f
l
ia wth , t
n
e
r
o
n
r
e
o
s
g
p on a
x
e
e
r
y
i
c
t
n
b
n
a
a
i
l
r
e
f
u
o
s
o fact
p
u
o
e
t
n
p
.
a
a
l
r
r
h
c
e
t
d the
+
u
w
o
o
1
o
r b =
Y to m ow
g
e
n
th tion
k
d
u
n qua
o
i
y
f
f
n
I
e
a
e
c
h
t
u
o
g
y
usin
6
8­1 Exploring Exponential Models 2011
April 13, 2011
7
8­1 Exploring Exponential Models 2011
April 13, 2011
Second, find a, the initial population.
In 2000, the population was 281, so a = 281.
Next, write the exponential function.
y = 281(1.0124)x
8
8­1 Exploring Exponential Models 2011
April 13, 2011
y = 281(1.0124)x
9
8­1 Exploring Exponential Models 2011
April 13, 2011
10
8­1 Exploring Exponential Models 2011
April 13, 2011
11
8­1 Exploring Exponential Models 2011
April 13, 2011
12
8­1 Exploring Exponential Models 2011
April 13, 2011
You can use an exponential function with 0 < b < 1 to model decay.
When b < 1, b is a decay factor.
An asymptote is a line that a graph approaches as x or y increases in absolute value.
13
8­1 Exploring Exponential Models 2011
April 13, 2011
Without graphing, determine whether each function represents exponential growth or exponential decay.
a. y = 100(0.12)x
b. y = 0.2(5)x
c. y = 16(½)x
14
8­1 Exploring Exponential Models 2011
April 13, 2011
Graph y = 24(1/2)x. Identify the horizontal asymptote.
15
8­1 Exploring Exponential Models 2011
April 13, 2011
16
8­1 Exploring Exponential Models 2011
April 13, 2011
17
8­1 Exploring Exponential Models 2011
April 13, 2011
Homework
page 434
(9 ­ 12, 16 ­ 22, 33 ­ 54 MOT)
18