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# 7.2

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### 7.2

1. 1. 7.2 PROPERTIES OFEXPONENTIALFUNCTIONS
2. 2. Transformations of ExponentialFunctions Note that the base of the parent is a variable,  Parent: therefore there are infinite “parents” within the Exponential Family  General Form:  Stretch:  Compression (shrink):  Reflection:  Horizontal Translation:  Vertical Translation:
3. 3. Graph each function as atransformation of its parent 1. Create a Table of Values for the parent 2. Plot the points and label the graph 3. 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
4. 4. Examples
5. 5. Examples
6. 6. Examples
7. 7. 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
8. 8. Continuously CompoundedInterestTo use this function:1. Identify the value of the variables2. Plug the known values into the equation3. Solve for the unknown value
9. 9. 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.
10. 10. Homework P447 #1 – 4 all, 7 – 27 odd, 28 – 31 all