Rivers do not flow at the same rate the year around. They tend to be full in the spring wh...

Rivers do not flow at the same rate the year around. They tend to be full in the spring when the snow melts and to flow more slowly in the fall. To take this into account, suppose the flow of the input river in Exercise 9 is

Our river flows at its maximum rate one-third into the year (i.e., around the first of April) and at its minimum around the first of October.

(a) Setting p = 2, and using this flow rate, use your numerical solver to plot the concentration for several choices of initial concentration between 0% and 4%. (You might have to reduce the relative error tolerance of your solver, perhaps to 5 × 10–12.) How would you describe the behavior of the concentration for large values of time?

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(b) It might be expected that after settling into a steady state, the concentration would be greatest when the flow was smallest (i.e., around the first of October). At what time of year does it actually occur?