Download Chapter 9-2

Chapter 9
Exponential and
Logarithmic
Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-1
1
Chapter Sections
9.1 – Composite and Inverse Functions
9.2 – Exponential Functions
9.3 – Logarithmic Functions
9.4 – Properties of Logarithms
9.5 – Common Logarithms
9.6 – Exponential and Logarithmic Equations
9.7 – Natural Exponential and Natural
Logarithmic Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-2
2
§ 9.2
Exponential Functions
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-3
3
Graph Exponential Functions
To Find the Inverse Function of a One-to-One Function
For any real number a > 0 and a ≠ 1,
f ( x)  a x
or
y  ax
is an exponential function
Examples of Exponential Functions
f ( x)  2 ,
x
y5 ,
x
1
g ( x)   
 2
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
x
Chapter 9-4
4
Graph Exponential Functions
Graphs of Exponential Functions
For all exponential functions of the form y = ax or f(x) =ax,
where a > 0 and a ≠ 1,
1. The domain of the function is (, )
2. The range of the function is (0, )
3. The graph of the function passes through the points
  1, 1 , (0,1), and (1, a).


a

Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-5
5
Graph Exponential Functions
Example Graph the exponential function y = 2x.
State the domain and range of the function.
The function is the form y = ax, where a = 2. First
construct a table of values.
continued
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-6
6
Graph Exponential Functions
Now plot these points and connect them with a
smooth curve.
The domain of this function is the set of all real
numbers, or (-∞,∞). The range is {y|y > 0} or (0,∞).
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-7
7
Solve Applications of Exponential Functions
Compound Interest Formula
The accumulated amount, A, in a compound interest
account can be found using the formula
 r
A  p 1  
 n
where p is the principal or the initial investment amount, r
is the interest rate as a decimal, n is the number of
compounding periods per year, and t is the time in years.
nt
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-8
8
Solve Applications of Exponential Functions
Example Nancy Johnson invests $10,000 in certificate
of deposit (CD) with 5% interest compounded
quarterly for 6 years. Determine the value of the CD
after 6 years.
The principal, p, is $10,000 and the interest rate, r, is
5%. Because the interest is compounded quarterly, the
number of compounding periods, n, is 4. The money is
invested for 6 years so t is 6. Substitute these values
into the formula.
continued
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-9
9
Solve Applications of Exponential Functions
r

A  p 1  
 n
nt
0.05 

 10,0001 

4 

24
 10,0001  0.0125
 13,473.51
4(6)
The original $10,000 has grown to about $13,473.51
after 6 years.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 9-10
10