Chapter 9.3, Problem 105E

Solve each problem. See Objective 3.

When a thermal inversion layer is 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 and that the pollutant disperses horizontally over a circular area. Suppose that t represents the time, in hours, since the factory began emitting pollutants ( $t=0$ represents 8 A.M.), and assume that the radius of the circle of pollution is $r\left(t\right)=2t$ miles. Let $A\left(r\right)=\pi r^2$ represent the area of a circle of radius r. Find and interpret $\left(A\circ r\right)\left(t\right)$.