A tank initially contains 80 liters of pure water. Brine containing 1/4 kg of salt per liter flows into the tank at a rate of 12 L/min, and the well-stirred mixture flows out of the tank at the same rate.
(a) Set up a differential equation for x(t), the amount of salt (in kg) present in the tank at time t (in min). Don't forget to specify the initial condition.
(b) Solve the differential equation to determine the amount of salt present in the tank at any time t.
(c) How much salt is present at the end of 20 minutes?
(b) How much salt is present in the long run? Justify.