Exploring Exponential Functions Examine patterns in exponential functions

Work with a partner. 1. Fold a sheet of notebook paper in half. Notice that the fold line divides the paper into 2 rectangles. 2. Fold the paper in half again. Now how many rectangles are there? 3. Continue folding the paper in half until you cannot make another fold. Keep track of your results in a table. Label your two columns NUMBER OF FOLDS and NUMBER OF RECTANGLES. 4. PATTERNS: What pattern do you notice in the number of rectangles as the number of folds increase? Explain your answer. 5. Suppose you could continue to fold the paper. Extend your table to include 10 folds. How many rectangles would be there?

Exploring Exponential Functions Number of Folds Number of Rectangles What did you notice in the number of rectangles as the number of folds increases? How rectangles would you have if you could fold your paper in half 10 times?

Example 1 Suppose there are 20 rabbits on an island and that the rabbit population can triple every half-year. HOW MANY RABBITS WOULD THERE BE AFTER 2 YEARS? WHAT KIND OF PROBLEM SOLVING STRATEGY COULD YOU USE TO HELP YOU ANSWER THIS QUESTION?

Exponential Functions Analyze the following graphs what characteristics do you see...think about domain and range, y- intercept, x-intercept, end behavior, increase or decrease.

What similarities and differences do you see? Compare the two graphs What similarities and differences do you see?