5. A tank initially contains 5kg of salt dissolved in 400L of pure water. This solution is kept thoroughly mixed and drains from the tank at a rate of AL/min. Simultaneously, a mixed solution of water with 2kg/L of salt is poured into the tank at the rate of 4L/min. Let y(t) be the amount of salt (in kg) in the tank at time t (in min). [5] (a) Set up the initial-value problem for the above situation. [5] (b) Solve the initial-value problem for y(t). [5] (c) After how many minutes does the amount of salt in the tank reach 200kg? Round your answer to 2 decimal places. [3] (d) Eventually (as t -+ co), what will the amount of salt in the tank be? [2] (e) In a few sentences, explain intuitively how your answer in part (d) makes sense. (Hint: Think about the concentration of salt poured into the tank and volume of the solution.)