When there is a thermal inversion layer over a city (as happens often in Los Angeles), pollutants cannot rise vertically but are trapped below the layer and must disperse horizontally. Assume that a factory smokestack begins emitting a pollutant at 8 a.m. Assume that the pollutant disperses horizontally, forming a circle. If t represents the time (in hours) since the factory began emitting pollutants (t = 0 represents 8 a.m.), assume that the radius of the circle of pollution is r(t) = 2t miles. 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 = 4.