7.* (Pollutant dispersal). Consider a chemical pollutant that enters a river that flows with constant speed u. Often it is assumed that the concentration of the pollutant c(x, t) is lost at a rate proportional to the concentration. a) Show that pollutant conservation is assured if Ctuc-ac where ac is the loss per unit volue of water if the concentration is c. b) Suppose that the river is initially pollutant free and a prescribed volume of pollutant is instantaneously released when t = 0 over the interval x [-L, L]. Determine the concentration levels at later times t. c) Suppose that rather than releasing all the pollutant at the time t = 0 and along part of the river, the pollutant is fed in continuously at the location x = 0 so that c(0, t) = ro for 0 < t < To and zero thereafter. Determine concentration levels downstream from the release point.