1. MAT 125 – Applied Calculus 5.1 – Exponential Functions

2. Today’s Class  We will be learning the following concepts today:  Exponential Functions & Their Graphs  Logarithmic Functions & Their Graphs  Properties Relating Exponential and Logarithmic Functions  Compound Interest  Effective Rate of Interest  Continuous Compounding of Interest Dr. Erickson 5.1 – Exponential Functions 2

3. Introduction  Exponential functions play an important role in many real-world applications.  What is an exponential function? Basic idea: a function with a variable as the exponent. Dr. Erickson 5.1 – Exponential Functions 3

4. 4 Definition Dr. Erickson

5. Laws of Exponents Dr. Erickson 5.1 – Exponential Functions 5

6. Simplify the expression. 1. 2. 3. 4. 5.1 – Exponential Functions 6 Example 1 Dr. Erickson

7. Example 2  Solve the equation for x. Dr. Erickson 5.1 – Exponential Functions 7

8. Example 3 Dr. Erickson 5.1 – Exponential Functions 8

9. Let’s continue with 5.2 & 5.3 Dr. Erickson 5.1 – Exponential Functions 9