1. Exploring Exponential Functions

2. Exponential Function The independent variable (x) is an exponent. f(x) = a b x “a” cannot be zero, “b” cannot be one and must be positive.

3. Exponential Functions “a” is the initial amount or the amount with which you start. “b” is the growth or decay factor “x” is the number of times it grows or decays.

4. Example 1 Suppose that two mice live in a farmhouse. If the number of mice quadruples every 3 months, how many mice will be in the house after 2 years? Make a table.

5. Example 1 How many mice at the beginning (initial amount)? How many mice after 3 months? How many mice after 6 months? How many mice after 9 months?

6. Example 1 Replace “a” with the initial amount (2 mice). Replace “b” with what is happening to the number of mice (Being multiplied by 4). Replace “x” with the number of 4 month periods (8).

7. Write an exponential function for… There are 200 cells in a jar. The number of cells triples every hour. y = 200 3 x There are 5 cats on an island. The number of cats doubles every three weeks. y = 5 2 x There is $800 in a savings account. The amount doubles every 8 years. y = 800 2 x

8. Evaluate each exponential function y = 3 x for x = 1, 2, and 4 y = 2.5 x for x = 2, 3 and 4 {3, 9, 81} {6.25, 15.625, 39.0625} (0.4, 0.16, 0.01024}

9. Graph y = 5(2) x Plug it into y=. Go to the table. Pick points that will fit on the grid.

10. Graph y = 3(1/2) x