$-0\mathrm{.}00020025$

$ln(\frac{399}{400})\frac{10}{125}$

Incorrect

At least one of the answers above is NOT correct.

$(1$ 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 $0\mathrm{.}5$ kilograms per liter is injected into the miding chamber at a constant rate of $r$ liters per minute. When the mixing process is started, the well$-$stirred midture is pumped from the chamber at a rate of $10r$ illers per minute.

$($a$)$ Develop a mathematical model for the mbing process. Let $Q$ represent the amount of dye in kilograms in the mixture.

$\frac{dQ}{dt}=k\frac{g}{m}in$

$($b$)$ The objective is to obtain a dye concentration in the outflow mixture of $0\mathrm{.}4$ 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 $4$ liters of clear liquid at time $t=0.$ How many minutes wit it take for the outflow concentration to rise to withip $-10$ K $.$ af the desirned enncentration of $0\mathrm{.}4$ kilograms per liter?

$t=$ min

Note: You can earn partial credit on this problem.

$$

$$ Viur ennee wese removier

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