Suppose that a 16L container has 8L of water and kool-aid mix with a kool-aid concentration of 0.25kg/L. Further suppose that a sweeter kool-aid mixture with a concentration of 0.5kg/L is pumped into the container at a rate of 4L/min. Let y(t) be the amount in kilograms of the kook-aid powder in the container where t is in minutes.
(a) If the resulting mixture is pumped out at the same rate as the new mixture is pumped in, state the initial value problem modeling the amount of kool-aid mix in the water. Solve this initial value problem.
(b) If instead the resulting mixture is pumped out 2L/min (the sweeter mixture is still being pumped in at 4L/min), state the initial value problem modeling the amount of kool-aid mix in the water. Solve this initial value problem.