question 1 Consider a tank used in certain experiments After

Consider a tank used in certain experiments. After one experiment the tank contains 180 liters of a dye solution with a concentration of 5 g/Liter. To prepare for tile next experiment, the tank is to be rinsed with fresh water flowing in at a rate of 2 liters/min, the well-stirred solution flowing out at the same rate. Find the concentration of the dye solution after the tank has been rinsed for 30 minutes.

Solution

Let Q be the amount of dye.

The equation is dQ/dt = (rate in) (rate out) = 0 (5)(Q/180) = 0.027Q

The form of the solution is Q(t) = Q0e^ (.0277t)

Q(30) = e^-0.833 = 2.3