Consider the mixing process shown in the figure. A mixing chamber initially contains 5 liters of a clear liquid. Clear liquid flows into the chamber at a rate of 10 liters per minute. A dye solution having a concentration of 0.25 kilograms per liter is injected into the mixing chamber at a constant rate of r liters per minute. When the mixing process is started, the well-stirred mixture is pumped from the chamber at a rate of 10+r liters per minute. (a) Develop a mathematical model for the mixing process. Let Q represent the amount of dye in kilograms in the mixture. dtdQ= kg/min (b) The objective is to obtain a dye concentration in the outflow mixture of 0.1 kilograms per liter. What injection rate r is required to achieve this equilibrium solution? r= L/min Would this equilibrium value of r be different if the fluid in the chamber at time t=0 contained some dye? (c) Assume the mixing chamber contains 5 liters of clear liquid at time t=0. How many minutes will it take for the outflow concentration to rise to within 4% of the desired concentration of 0.1 kilograms per liter? t= min