A liquid phase irreversible reaction: $A_{{?}_{?}}{?}_{{?}_{?}}{?}_{?}>B$ takes place in a CSTR of volume $V_T.$ The reactor is initially empty. At $t=0,$ a solution of species $A$ at concentration $C_{A_0}$ flows into the reactor at a constant volumetric flow rate of $Q_{in}.$ No liquid leaves the reactor until the liquid volume reaches a value of $V_T.$ The rate of reaction is given by

$r=k{C}_A$

If the reaction takes place under isothermal conditions, express the concentration of species A within the reactor as a function of time.