$29\mathrm{.}1.$ A culture of $E.$ coli was grown on lactose in a mixed flow reactor liter$)$ using various flow

rates of a $C_{AO}=160mg$ lactose$/$liter feed. The following results were obtained:

Find a rate equation to represent this growth. Note, species A is the substrate.

$($b$)$ E$.$ coli lives and grows on mannitol with the following kinetics

$r_C=\frac{1\mathrm{.}2C_A{C}_C}{C_A+2},C_A=gm$ mannitol $\frac{?}{m^3},Y_{\frac{C}{A}}=0\mathrm{.}1gm$ cells $\frac{?}{gm}$ mannitol

i$.$ Find the outlet concentration of cells from the reactor when $1\frac{m^3}{h}r$ of mannitol solution

$g\frac{m}{m^3})$ is fed directly to a mixed flow reactor of volume

$V=5m^3$

ii$.$ Determine the dilution rate at wash$-$out $(D_{\text{m}\text{a}\text{x}})$ and the dilution rate for maximum cell

production $)$