A wastewater with a BODL of $S=250m\frac{g}{L}$ undergoes aerobic biodegradation in a batch reactor that is seeded with an initial active biomass concentration of $x_a=2mg$ VSS $\frac{a}{?}$ L$.$ You can assume that the following Monod kinetic parameters apply: $q_{\text{m}\text{a}\text{x}}=15g$ BOD $\frac{?}{g}$ VSS ${?}_a*d,Y=0\mathrm{.}50g$ VSS $\frac{a}{g}BO{D}_L,$ comparison to the biomass synthesis rate$).$ Determine the BOD Loncentrations $(S)$ and active biomass concentrations $(x_a)$ after $t=0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,$ and $0\mathrm{.}68$ days.

The same wastewater as in Problem $6($above$)$ is treated in a theoretical ideal plug flow reactor $($i$.$e$.,$ with zero dispersion$)$ with no effluent recycle or biomass settling. You can again assume that $S=250$mgBO$\frac{D}{L}$ and $x_a=2mgVS\frac{S_a}{L}.$ What would be the effluent $BO{D}_{\text{l}\text{l}\text{c}\text{o}\text{r}\text{n}\text{e}\text{r}}$concentrations $(S)$ and active biomass concentrations $(x_a)$ at HRTs of $=0\mathrm{.}2,0\mathrm{.}4,0\mathrm{.}6,$ and $0\mathrm{.}68$ days?