Consider the mixing process shown in the figure. A mixing chamber initially contains 2 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. $\dfrac{dQ}{dt} =$ kg / min (b) The objective is to obtain a dye concentration in the outflow mixture of 0.2 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? Choose yes no maybe (c) Assume the mixing chamber contains 2 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 0.2 kilograms per liter? $t =$ min

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