Q$1)(40$P$)$ At a temperature of $37C,$ E$.$Coli bacteria are grown in an aerobic environment in a broth medium at $pH7\mathrm{.}0.$ The reactor type used is a batch reactor. Assumptions:

a$)$ Ignore the terms maintenance or endogenous respiration.

b$)$ Accept that the cells do not lose their vitality.

Derive the formula for cell growth.

Find the lag phase.

Using the data in Table $1,$ calculate $($specific growth rate$)$ in $mi{n}^{-1}.$

Calculate the time $(t_d)$ it takes to double the biomass concentration.

Table $1.$ Experimental data

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