A stirred$-$tank blending system initially is full of water and is being fed pure water at a constant flow rate, q$.$ At a particular time, an operator shuts off the pure water flow and adds caustic solution at the same volumetric flow rate q but with concentration c$\_$i$.$ If the liquid volume V is constant, the dynamic model for this process is V dc $/$ dt $+$ qc $=$ qc$\_$i with c$(0)=20$ kg$/$m$^3$ What is the concentration response of the reactor effluent stream, c$($t$)?$ Sketch it as a function of time. Data: V $=3$m$^3$; q $=0\mathrm{.}2.$m$^3$min; c$\_$i $=60$ kg$/$m$^3$