**Let’s Summarize**

This is what we have learned about exponential models:

The general form of an *exponential model* is *y = C · b ^{x}*.

- Exponential models are nonlinear. More specifically, exponential models predict that
*y*increases or decreases by a constant percentage for each 1-unit increase in*x*.

*C*is the*initial value*. It is the*y*-value when*x*= 0. It is also the*y*-intercept.

*b*is the*growth factor*or*decay factor*.*b*is always positive.- If
*b*is greater than 1,*b*is a growth factor. In this case, the association is positive, and*y*is increasing. This makes sense because multiplying by a number greater than 1 increases the initial value. From the growth factor, we can determine the percent increase in*y*for each additional 1-unit increase in*x*. - Similarly, if
*b*is greater than 0 and less than 1,*b*is a decay factor. In this case, the association is negative, and*y*is decreasing. From the decay factor, we can determine the*percentage decrease*in*y*for each additional 1-unit increase in*x*.

- If

Let’s compare the general form of an exponential model to the general form for a *linear model:* *y* = *a* + *bx*.

- In the linear model,
*a*is the*initial value*. It is the*y*-value when*x*= 0. It is also the*y*-intercept.

*b*is the*slope*. From the slope, we can determine the*amount*and*direction*the*y*-value changes for each additional 1-unit increase in*x*. When*b*is positive, there is a positive association, and*y*increases. When*b*is negative, there is a negative association, and*y*decreases.