A $300$L batch process uses the yeast Pichia pastoris to produce human growth hormone $($HGH$).$ The initial yeast biomass concentration is $0\mathrm{.}1\frac{g}{L}.max=\frac{0\mathrm{.}35}{h},$ the specific glucose uptake rate is $q_{\text{s}\text{u}\text{b}\text{s}\text{t}\text{r}\text{a}\text{t}\text{e}}=18$mmol glucose $\frac{?}{gcd}\frac{w}{h},$ and the specific HGH production rate is $q_{HGH}=0\mathrm{.}1$mmo$\frac{l}{g}cd\frac{w}{h}.$ The reactor initially contains $90\frac{g}{L}$ of glucose. Assume the lag phase is minimal due to optimized seed culture handling.

At $t=7$ hours:

a$)$ How does the volumetric and total HGH rate change with time?

b$)$ When is the glucose exhausted?