An oil well off the Gulf Coast is leaking, with the leak spreading oil over the surface as a circle. At any time t (in minutes) after the beginning of the leak, the radius of the circular oil slick on the surface is r(t) = t² feet. Let A(r) = πr² represent the area of a circle of radius r.
(a) Find and interpret A[r(t)].
(b) Find and interpret D_t A[r(t)] when t = 100.