A tank contains 80 kg of salt and 2000 L of water. Pure water enters a tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 6 L/min.
(a) Write an initial value problem for the amount of salt, y, in kilograms, at time t in minutes:
dy/dt = (kg/min) y(0) = kg.
(b) Solve the initial value problem in part (a)
y(t) = kg.
(c) Find the amount of salt in the tank after 3 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)