A tank contains 50 kg of salt and 1000 L of water. Water containing 0.3 kg/L of salt enters the tank at the rate 12 L/min. The solution is mixed and drains from the tank at the rate 4 L/min. A(t) is the amount of salt in the tank at time t measured in kilograms.
(a) A(0) = (kg)
(b) A differential equation for the amount of salt in the tank is = 0. (Use t,A, A', A'', for your variables, not A(t), and move everything to the left hand side.)
(c) The integrating factor is
(d) A(t) = (kg)
(e) 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