A tank initially contains 10kg of salt dissolved in 250L of pure water. This solution is kept thoroughly mixed and drains from the tank at a rate of 5L/min. Simultaneously, a mixed solution of water with 2kg/L of salt is poured into the tank at the rate of 5L/ min. Let y(t) be the amount of salt (in kg) in the tank at time t ( in min). (a) Set up the initial-value problem for the above situation. (b) Solve the initial-value problem for y(t). (c) After how many minutes does the amount of salt in the tank reach 100kg? Round your answer to 2 decimal places. (d) Eventually (as t -> co), what will the amount of salt in the tank be? (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.)