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