Pollution in a lake. consider a lake with a stream flowing out of it and a nearby factory dumping pollution into it. without worrying about the modeling details yet, the mass of pollution in the lake is represented by dp dt = − r/v p + f, where p is the mass of pollution in the lake (kg), r is the flow rate of the stream (m3/sec), v is the volume of the lake (m3) and f is the mass of pollution dumped per time by the factory (kg/sec). treat r, v and f as constants. use an integrating factor to solve the ode in general form. find the constant of integration if the initial condition is p(0) = a, and write the solution for p(t) in a clean, final form.