A stirred tank reactor system with operation conditions that volume: $4m^3,$ flow rate $q=2m^3/$min$,$ feed concentration $C_i=1$kgmol$\frac{e}{m^3}$; no chemical reaction occurs in the tank. $($a$)$ build up an ODE model; $($b$)$ Laplace transformed Model $($c$)$ if the $C_i$ is suddenly changed from $1$ to $5$kgmol$\frac{e}{m^3},$ what will be dynamic response of concentration $C(t)$ in the tank?