$(2$ points$)$ Using the information about an active sludge treatment stage given below, determine the sludge age $($mean cell residence time$).$

Suspended solids in effluent negligible

Yield coefficient $=0\mathrm{.}4$

bacterial decay rate $=0\mathrm{.}04d^{-1}$

effluent $BO{D}_5=10m\frac{g}{L}$

$\frac{F}{M}=0\mathrm{.}33m\frac{g}{m}g*d$

$BO{D}_5$ after primary settling $=150m\frac{g}{L}$

$MLVSS=1700m\frac{g}{L}$

$MLSS=1\mathrm{.}4(MLVSS)$

$Q=0\mathrm{.}0796\frac{m^3}{s}$

$V=1806m^3$

aeration period $=0\mathrm{.}5d$