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Question: 5 pollution in a lake consider a lake with a...

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5) 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 byP+ F, where P is the mass of pollution in the lake (kg), ris the flow rate of the stream (m/sec), V is the volume of the lake (m3) and F is the mass of pollution dumped per time by the factory (kg/see). Treat r, V and F as constants. Use an integrating factor to solve the ODE in general form. Find the constaut of integration if the initial condition is PO) A, and write the solution for P(t) in a clean, final form.

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