A well stirred vessel of volume V initially contains fresh water. Dirty water of concentration C_0+cos(wt) (mass/volume) is fed to it at the rate of q (volume/time), where w is the frequency of concentration of the feed stream. Assuming that the exit flow rate is also q and that the density of the tank does not appreciably change the tank volume from V, find the exit concentration as a function of time including the long time solution. Do the problem by scaling the concentration C with C_0 and time with t, where t = V/q.