mat 125 applied calculus 5.1 exponential functions

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MAT 125 – Applied Calculus 5.1 – Exponential Functions

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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

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Page 1: MAT 125  Applied Calculus 5.1  Exponential Functions

MAT 125 – Applied Calculus5.1 – Exponential Functions

Page 2: MAT 125  Applied Calculus 5.1  Exponential Functions

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

Page 3: MAT 125  Applied Calculus 5.1  Exponential Functions

5.1 – Exponential Functions

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

Page 4: MAT 125  Applied Calculus 5.1  Exponential Functions

4

5.1 – Exponential Functions

Definition

Dr. Erickson

Page 5: MAT 125  Applied Calculus 5.1  Exponential Functions

5.1 – Exponential Functions

5 Laws of Exponents

Dr. Erickson

Page 6: MAT 125  Applied Calculus 5.1  Exponential Functions

5.1 – Exponential Functions

6

Simplify the expression.

1.

2.

3.

4.

Example 1

Dr. Erickson

Page 7: MAT 125  Applied Calculus 5.1  Exponential Functions

5.1 – Exponential Functions

7 Example 2

Solve the equation for x.

Dr. Erickson

Page 8: MAT 125  Applied Calculus 5.1  Exponential Functions

5.1 – Exponential Functions

8 Example 3

Dr. Erickson

Page 9: MAT 125  Applied Calculus 5.1  Exponential Functions

5.1 – Exponential Functions

9 Let’s continue with 5.2 & 5.3

Dr. Erickson