Q$1.(20$ marks$)$A reaction A $->$ R takes place in a constant volume isothermal CSTR$.$ The component mass balances are: where CAi $($input considered as a variable$)$ and CRi $($constant$)$ is the feed concentration of A and R$,$ respectively, while CA and CR are the concentrations of A and R in the outlet stream, respectively.a$.$ Linearize the equations around the design SS $($CAiS$,$ CAs, CRs$)$ and put them in deviation variable form.b$.$ Find the transfer function between CR and CAi.c$.$ Does the above TF correspond to an overdamped or underdamped system? Explain.