=1. (6pts) a. An initially clean lake (c(0) = 0) maintains a constant volume of V = 400,000 m³ of water. Above this lake is a stream feeding in from agricultural fields that have been sprayed with a new pesticide. This stream has a flow rate of f 800 m³/day. With several measurements it is found that the pesticide concentration in the stream satisfies p(t) = 20e-0.0005 µg/m³. Assume that this is a well-mixed lake with a stream flowing out at the same rate of f (with the pesticide in the outflowing stream equal to the concentration in the lake). Write a differential equation describing the concentration of pesticide in the lake (c(t)) and solve this differential equation. b. Create a graph of the solution, showing the concentration of the pesticide in the lake as a function of time. When is the concentration of the pesticide at its maximum concentration and what is that concentration? (Slides Linear 24-35)

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