1. Exponential and Logarithmic Functions
Chapter 9
Exponential and Logarithmic Functions

2. 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
Chapter 1 Outline

3. Exponential Functions
§ 9.2
Exponential Functions

4. Graph Exponential Functions
To Find the Inverse Function of a One-to-One Function
For any real number a > 0 and a ≠ 1,
is an exponential function
Examples of Exponential Functions

5. 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,
The domain of the function is
The range of the function is
The graph of the function passes through the points

6. 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

7. 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,∞).

8. Solve Applications of Exponential Functions
Compound Interest Formula
The accumulated amount, A, in a compound interest account can be found using the formula
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.

9. 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

10. Solve Applications of Exponential Functions
The original $10,000 has grown to about $13, after 6 years.