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$)\frac{?}{(g\text{c}\text{e}\text{l}\text{l}\text{s}*h)}$