This is a modified version of problem $6\mathrm{.}4($problem $6\mathrm{.}2$ in the $2^{nd}$ edition$)$ in the

textbook.

The growth of a microbial population as a function of $pH$ is given by$,$

$=\frac{1}{x}\frac{dx}{dt}=\frac{{}_{m}S}{K_S(1+\frac{H^{+}}{K_1})+S}$

a$.$ Propose an experimental method for data collection and the accompanying plots

and calculations to estimate the constants ${}_m,K_s,$ and $K_{\text{I}}.$

b$.$ Hand$-$sketch the double$-$reciprocal plot of $\frac{1}{}$ vs$.\frac{1}{S}$ with changes to $pH.$

c$.$ Is $pH$ inhibiting cell growth? If inhibition exists, what type of inhibition is this?

Explain your answer.A batch fermentation of an aerobic bacterium growing on glucose gives the results shown in the table below,The following data were obtained for the growth an aerobic bacterium in a batch reactor.

$\backslash$table$[[$Time $($hr$),x(\frac{g}{L}),S(\frac{g}{L})$

$\backslash$table$[[$time $(hr),x(\frac{g}{L}),S(\frac{g}{L}),P(m\frac{g}{L})$