Answer Happy

2. A tank contains 40 liters of a saltwater solution. The solution contains 4 kg of salt. A second saltwater solution containing 0.5 kg of salt per liter is added to the tank at 6 liters per minute. The solution in the tank is kept thoroughly mixed and drains from the tank at 6 liters per minute. (a) How much salt is in the tank after t minutes? Sketch a graph of this function. (b) What is the concentration of the solution in the tank after t minutes? (c) Will there ever be 15 kg of salt in the tank?
(d) How much salt will there be in the tank after a long time has passed? (e) Find all equilibria of your differential equation and determine their stability. (f) How do your answers to parts (d) and (e) relate to each other?