#### Problem 15E

15. A spherical balloon is being inflated. Find the rate of increase of the surface area $\left(S=4 \pi r^{2}\right)$ with respect to the radius $r$ when $r$ is (a) $1 \mathrm{ft}$, (b) $2 \mathrm{ft}$, and (c) $3 \mathrm{ft}$. What conclusion can you make?