1. Exponential Models Recall that an exponential function is of the form f ( x ) = ab x , where a ≠ 0, b >0, and b ≠ 1. When using an exponential function as a model for a real-life situation, x often represents time. Since f (0)= a , a is referred to as the initial value of the dependent variable. b , on the other hand, is known as the growth factor . Initial Value Growth Factor

2. How do exponential models compare with linear models? The parameter that controls the “growth” of each type of functions works differently in each case. A linear model exhibits constant increase/decrease , which is determined by m . An exponential model exhibits constant percentage change , which is determined by b . Rate of increase/decrease Growth factor (% change)

3. How do exponential models compare with linear models? To find an equation of a line, we need two points. This is related to the fact that there are two parameters in the equation: m and b . How many points do you think we need to determine an exponential equation?

4. We can use the points to write two equations: If we divide the second equation by the first: Finally, we can find a : Let’s find an exponential equation that includes the points (2, 6) and (4,10): We know the equation has this form:

5. We can use the points to write two equations: If we divide the second equation by the first: Finally, we can find a : Let’s find an exponential equation that includes the points (2, 6) and (4,10): We know the equation has this form:

6. We can use the points to write two equations: If we divide the second equation by the first: Finally, we can find a : Let’s find an exponential equation that includes the points (2, 6) and (4,10): We know the equation has this form: Can’t my calculator do this for me???