Question $4(20$ pts$).$ The wastewater treatment pond in the below figure is slowly accumulating a chemical $x$ entering in the influent. a$)$ write a differential equation for

the accumulation of $x$ in the pond, assuming the system is completely mixed, evaporation can be described in terms of a mass transfer coefficient $($specify the dimension of the coefficient$),$ and the pond is leaking water and chemical at a rate proportional to $bC,$ where $b$ is a dimensionless coefficient between $0$ and $1$ and $C$ is the bulk concentration of $x$ in water. The pond volume is considered variable. b$)$ Assume that the evaporation rate is small, and that inflow is interrupted for a period of

time but the leakage continues from the bottom. Derive an equation that describes the concentration of $x$ in the pond.