If the radius of a circle increases from $r_1$ to $r_2$, then the average rate of change of the area of the circle is

A. less than $2\pi r_2$.

B. greater than $2 \pi r_1$.

C. equal to $2\pi \frac{r_1+r_2}{2}$.

D. all of the above.

In the answer box below, explain your reasoning for the choice you made above. Use complete sentences and correct grammar, spelling, and punctuation. Be specific and detailed. Write as if you were explaining the answer to someone else in class.