Chemical Reactor Engineering Problem!

Please answer this question as soon as possible with specific explanation.

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The growth of cells of a certain bacteria can be expressed in terms of the logistic growth law:

$r_g={}_m(1-\frac{C_c}{C_m})C_C$

where $C_c$ is the concentration of cells $($in g$/$dm$^3),$ and ${}_m=0\mathrm{.}5h^{-1}$ and $C_m=20\frac{g}{d}{m}^3$ are constants of

the rate law. For the purposes of this problem the concentration of substrate $(C_s)$ is in large excess and

hence can be considered constant.

$($a$)$ For a batch reactor with an initial inoculation of $2g$ of cells into the $2d{m}^3$ reactor, plot the concentration

of cells versus time for $0t24h.$

$($b$)$ For a Chemostat with $C_{c0}=0\frac{g}{d}{m}^3,$ determine the washout dilution rate and the dilution rate that

maximises production of the bacteria.