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:
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
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 CompoundedInterestTo 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