This problem has three parts. This is part $1.$

For a mean cell residence time of $5$ days, maximum specific rate of substrate utilization of $16$ mg BODL$/$mg VSSa$-$d$,$ half$-$saturation constant of $20$ mg$/$L$,$ endogenous decay coefficient of $0\mathrm{.}15$ d$-1,$ true yield for cell synthesis of $0\mathrm{.}5$ mg VSSa$/$mg BODL, biodegradable fraction of $0\mathrm{.}80,$ input concentration of inert biomass of $50$ mg VSSi$/$L and an influent substrate concentration of $400$ mg BODL$/$L$.$