3. Water flows into and out of a 1,000 liter (L) tank at a constant rate of 4 L/min. The tank initially contains pure water, but then the water coming in has a concentration of 10 grams/L of salt. The solution in the tank is well-mixed so that the concentration of salt in it is uniform at all times. (a) Set up the differential equation for the amount of salt, I - r(t), in the tank at time t. Include the initial condition in order to make it an initial value problem. [6 points] (b) Solve the differential equation to find an expression for z(t). Be sure to evaluate the constant of integration using the initial condition. [8 points] (c) How long will it take for the amount of salt in the tank to be 5000 g? [2 points]