** Cleaning Up Lake Erie ** Lake Erie has a volume of roughly 100 cubic miles, and its equal inflow and outflow rates are 40 cubic miles per year. At year

= 0, a certain pollutant has a volume concentration of 0.05%, but after that the concentration of pollutant flowing into the lake drops to 0.01%. Answer the following questions, assuming the pollutant leaving the lake is well mixed with lake water.

(a) What is the differential equation satisfied by the volume

(in cubic miles) of pollutant in the lake?

cubic miles per year.

????????

(b) What is the volume

(in cubic miles) of pollutant in the lake at time

?

(

) = cubic miles.

(c) How long (in years) will it take to reduce the pollutant concentration to 0.02% in volume?

= years.