A stirred tank reactor system $($CSTR$)$ with operation conditions that volume V$=4$m$3,$ flow rate q $=2$m$3/$min$,$ feed concentration Ci $=1$kgmol$/$m$3.$ The $1$st order reaction occurs in the tank with rate constant k$=0\mathrm{.}1$ min$-1.$

a$)$ Build up an ODE model for this CSTR system

b$)$ Laplace transformed model

c$)$ Solve this model to show the exit concentration C$($t$)$ with respect to time