Lake Erie has a volume of roughly 100 cubic miles and its equa1 inflow and outflow rates are 40 cubic miles per year. At year t = 0 a certain pollutant has a volume concentration of 0.05% but after that t h e concentration of pollutant flowing into the lake drops to 0.01 %. Answer the following questions assuming that the pollutant leaving the lake is well mixed with lake water.
(a) What is the IVP satisfied by the volume V (in cubic miles) of pollutant in the lake?
(b) What is the volume V of pollutant in the lake at time t?