7.2 PROPERTIES OF EXPONENTIAL FUNCTIONS

Transformations of Exponential Functions

Parent:

General Form: Stretch: Compression (shrink): Reflection: Horizontal Translation: Vertical Translation:

Note that the base of the parent is a variable, therefore there are infinite “parents” within the Exponential Family

Graph each function as a transformation of its parent

1. Create a Table of Values for the parent2. Plot the points and label the graph3. If the transformation contains a stretch,

compression, or reflection: Create a Table of Values for the transformed function (use the same x-values) and Plot the points and label the graph

4. If the transformation contains a simple horizontal or vertical translation: move the parent points appropriately

Examples

Examples

Examples

The Number e

The Number e is an irrational number approximately equal to 2.71828

Exponential functions with base e are called natural base exponential functions. These exponential functions have the same

properties as other exponential functions To graph functions with base e, use the “e”

key on the calculator to get a decimal approximation

Continuously Compounded Interest

To use this function:1. Identify the value of the variables2. Plug the known values into the equation3. Solve for the unknown value

Example (p447)

Suppose you won a contest at the start of 5th grade that deposited $3000 in an account that pays 5% annual interest compounded continuously. How much will you have in the account when you enter high school 4 years later? Express the answer to the nearest dollar.

Homework

P447 #1 – 4 all, 7 – 27 odd, 28 – 31 all