Suppose that salty water containing 0.3kg/L runs into a tank at a rate of 10L/min. The tank is initially filled with 400L of solution containing 2kg of salt. Inside the tank, the mixture is kept uniform by stirring. There is a second pipe leaving the tank where the water and salt mixture flows out at a rate of 10L/min. let A(t) denote the amount of salt in the tank at time t.

(a) Write down an Initial Value Problem in term of A(t) that models this situation 

(b) Solve the IVP 

(c) Use your solution to the IVP to argue what happens as t → ∞.