1
MA 15200
Lesson 27
Section 4.1
We have discussed powers where the exponents are integers or rational numbers.
There
also exists powers such as
3
2
.
You can approximate powers on your calculator using
the power key.
On most oneliner scientific calculators, the power key looks like
Enter the base into the calculator first, press the power key, enter the exponent, and press
enter or equal.
Ex 1: Approximate the following powers to 4 decimal places.
32
4.8
)
2
_________________
)
(2.3)
________________
a
b
I
Exponential Functions
A Basic
exponential function
f
with base
b
is defined by
( )
or
xx
f x
b
y
b
, where
b
is
a positive constant other than 1 and
x
is any real number.
A calculator may be needed to evaluate some function
values of exponential functions.
(See example 1 above.)
Many real life situations model exponential functions.
One
example given in your textbook models the average amount spent
(to the nearest dollar) at a shopping mall after
x
hours and is
( )
42.2(1.56)
x
fx
.
The base of this function is 1.56.
Notice there
is also a ‘constant’ (42.2) multiplied by the power.
Be sure to follow the order of
operations; find the exponent power first, then multiply that answer by the 42.2.
Suppose you wanted to find the amount spent in a mall after browsing for 3 hours.
Let
x
= 3.
3
(3)
42.2(1.56)
42.2(3.796416)
160.2087552
f
To the nearest dollar, a person on average would spend $160.
x
y
The following are
not
exponential functions.
Why?
3
( )
( ) 1
( )
( 4)
( )
x
f x
x
f x
f x
f x
x
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II
Graphing Exponential Functions
Ex 2: Graph each exponential function.
x
y
a
2
3
)
x
x
f
b
3
1
)
(
)
There are several exponential graphs shown in figure 4.4 on page 415 of the text.
After
examining several graphs, the following characteristics can be found.
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 Fall '09
 Exponential Function, Exponents, Integers, Natural logarithm

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