When we calculate the average rate of change for a linear function, no matter what interval we pick, the value of the rate of change is the same. A constant rate of change is an important feature of linear functions! When a linear function is represented by a graph, the slope of the line is the rate of change of the function.

Exponential functions also have important features. We've learned about exponential growth and exponential decay, both of which are characterized by a constant quotient over equal intervals. But what does this mean for the value of the average rate of change for an exponential function over a specific interval?

The average rate of change of $A$ from the start of treatment to Week 2 is about -107 square yards per week because $\dfrac{A(2)-A(0)}{2-0} \approx \text-107$. The average rate of change of $A$ from Week 2 to Week 4, however, is only about -12 square yards per week because $\dfrac{A(4)-A(2)}{4-2} \approx \text-12$.

The negative average rates of change show that $A$ is decreasing over both intervals, but the average rate of change for the time during Weeks 0 to 2 indicates that the values are decreasing more rapidly than during Weeks 2 to 4 due to the effect of the decay factor. For an exponential function with a growth factor greater than 1, the values for the average rate of change of each interval are positive, with the second interval increasing more quickly due to the effect of the growth factor.