This is a problem in batch processing of materials using a mixing tank. the mixing tank has inflow and outflow tubes and a stirrer that keeps the concentration uniform at all points in the tank. the tank is initially filled by a volume v of solution, formed by dissolving a given solute in a solvent, with concentration c0(measured in kg/l)? ; the inflow tube carries a solution of different concentration cin than the initial concentration; the volumetric flowrate is qin the outflow flowrate is qout and, due to the well-mixed assumption, the outflow concentration has the same concentration as the instantaneous concentration of the tank. (i) derive the differential equation governing the instantaneous concentration in the tank; (ii) assume the tank volume is 1000 l, the volume initially contains 10 kg of salt, the rate of inflow is 2 l/s, the inflow concentration is 0.005 kg/l and that qin = qout (in other words, the outflow pipe carries away the overflow). calculate and plot the instantaneous concentration of salt c(t); (iii) calculate the time required to produce a solution of concentration 0.008 kg/l.