A tank contains 100 kg of salt and 1000 L of water. Pure water enters a tank at the rate 6 L/min. The solution is mixed and drains from the tank at the rate 3 L/min. (a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes: dy (kg/min) y(0)=k kg. dt (b) Solve the initial value problem in part (a) y(t) = kg. (c) Find the amount of salt in the tank after 4 hours. amount = (kg) (d) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.) concentration = (kg/L)