Consider a tank used in certain hydrodynamic experiments. After
one experiment the tank contains 200 L of a dye solution with a
concentration of 1 g/L. To prepare for the next experiment, the
tank is to be rinsed with fresh water flowing in at a rate of 2.5
L/min, the well-stirred solution flowing out at 2 L/min.
(a) Suppose that (as before) there is initially 200L of the dye
solution in the tank, and assume that the tank holds 300L. What is
the expression for the volume of fluid in the tank, and after how
many minutes is the tank full?
(b) How long does it take to reach the desired concentration of
1% of its original value?