When a thermal inversion layer is over a city (as happens 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 over a circular area. 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 pollutants at time t is r(t) = 2t miles. Let A(r) = πr² represent the area of a circle of radius r.

(a) Find (A ° r)(t). 

(b) Interpret (A ° r)(t).

(c) What is the area of the circular region covered by the layer at noon?