(Solved): point) Consider the mixing process shown in the figure. A mixing chamber initially contains 4 liter ...

point) Consider the mixing process shown in the figure. A mixing chamber initially contains 4 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 $$0.5$$ 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. $$\frac{dQ}{dt}=$$ $$\mathrm{kg}/\min$$ (b) The objective is to obtain a dye concentration in the outflow mixture of $$0.2$$ kilograms per liter. What iniection rate $$r$$ is required to achieve this equilibrium solution? $$r=$$ $$\mathrm{L}/\min$$ 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 4 liters of clear liquid at time $$t=0$$. How many minutes will it take for the outflow concentration to rise to within $$2\%$$ of the desired concentration of $$0.2$$ kilogramstper liter? $$t=$$