A stone is thrown into a pond. A circular ripple is spreading over the pond in such a way that the radius is increasing at the rate of 6.5 feet per second.

a) Find a function, r(t), for the radius in terms of t. (3 points)

b) Find a function, A(r), for the area of the ripple in terms of r. (3 points)

c) Evaluate the composition of (A o r)(t). Show your work. (5 points)

d) Interpret the result of (A o r)(t). (2 points)

e) Find the time, in seconds, when the area of the circular ripple is 500 sq. ft. (Show your work and round to 1 decimal point). (5 points)