$(15$ pts$)$ A lake has a volume of $10{10}^6{m}^3$ and is being supplied with water from a stream with a flow rate of $1\mathrm{.}0\frac{m^3}{s}$ and a pollutant concentration of $10m\frac{g}{L}.$ An additional second stream is discharging $0\mathrm{.}2\frac{m^3}{s}$ of wastewater with a pollutant concentration of $100m\frac{g}{L}$ into the lake. The microorganisms living in the lake are capable of decomposing pollutants at a decay rate coefficient of day$),$ and there are no other inflows or outflows of water mentioned. Find the equilibrium concentration of pollutants in the lake if it is modeled as a CSTR reactor.