- 9 A An Initially Clean Lake C 0 0 Maintains A Constant Volume Of V 400 000 M3 Of Water There Are Two Streams E 1 (161.51 KiB) Viewed 22 times
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9. a. An initially clean lake (c(0) = 0) maintains a constant volume of V = 400,000 m3 of water. There are two streams entering this lake with differing concentrations of agricultural pesticide. The first stream has a flow rate of f1 = 300 m3/day with a pesticide concentration of Q1 = 12 ug/m². A second stream has a flow rate of f2 = 500 m3/day with a pesticide concentration of Q2 = 4 ug/m². Assume that this is a well-mixed lake with a stream flowing out at a rate of f3 = 800 m3/day (with the pesticide in that stream equal to the concentration in the lake). Write a differential equation describing the concentration of pesticide in the lake and solve this differential equatio b. Determine how long until the lake has a concentration of 4 ug/m3 of pesticide. Also, find the limiting concentration of pesticide in this lake. c. The pollution results in a declining reproduction for an algal species, which would normally bloom this time of year. With the pollution affecting the algal population through its cell surface, the population satisfies the following growth model: dP = (0.08 - 0.002 t) P3/4, P(0) dt = 1296. Solve this differential equation. Find when this model predicts that the population achieves a maximum and what that maximum population is. Determine the population at t = 100.