A tank initially contains S0 of salt dissolved in 200 gal of water, where S0 is some pos...

A tank initially contains S₀ of salt dissolved in 200 gal of water, where S₀ is some positive number. Starting at time t = 0, water containing 0.5 lb of salt per gallon enters the tank at a rate of 4 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank at time t show that the limiting concentration- that is —-is 0.5 lb/gal.