Example:

Glucose$-$to$-$ethanol fermentation is to be carried out in a batch reactor using an organism such as Saccharomyces cerevisiae. Derive required equations to plot the concentrations of cells, substrate, and product and growth rates as functions of time. The initial cell concentration is $1\mathrm{.}0\frac{g}{d}{m}^3$ and the substrate $($glucose$)$ concentration is $250\frac{g}{d}{m}^3.$

$C_p^{**},=93\frac{g}{d}{m}^3,Y_{\frac{c}{s}},=0\mathrm{.}08\frac{g}{g}$

$n,=0\mathrm{.}52,Y_{\frac{p}{s}},=0\mathrm{.}45\frac{g}{g}(est.)$

${}_{\text{m}\text{a}\text{x}},=0\mathrm{.}33h^{-1},Y_{\frac{p}{c}},=5\mathrm{.}6\frac{g}{g}(est.)$

$K_s,=1\mathrm{.}7\frac{g}{d}{m}^3,k_d,=0\mathrm{.}01h^{-1}$

$m,=0\mathrm{.}03(g$ substrate$)\frac{?}{(g\text{c}\text{e}\text{l}\text{l}\text{s}*h)}$

$72$