- 2. A lake has a total volume 1000 (cubic units). A freshwater stream flows into the lake at a rate 10 cubic units per

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2 A Lake Has A Total Volume 1000 Cubic Units A Freshwater Stream Flows Into The Lake At A Rate 10 Cubic Units Per 1 (152.6 KiB) Viewed 23 times

- 2. A lake has a total volume 1000 (cubic units). A freshwater stream flows into the lake at a rate 10 cubic units per day, and flows out at the other end at the same rate. There is no pollutant in the lake until (at t = 0, say), a local company upstream is allowed to start pumping into the stream a solution containing a by-product of its manufacturing process; the pump runs every other day, pumping at a rate of 5 cubits units of solution per day, with a pollutant concentration at 0.01 kg per cubic unit of volume. a. Find and solve an initial-value problem for the amount x(t) of pollutant in kg in the lake at time t (days). (Note: the “forcing” term will be periodic and discontinuous.) b. Ecologists warn that if the pollutant concentration gets to the level of 4 x 10-5 kg per cubic unit, then the wildlife relying on the lake will suffer. Does the model predict that the pollutant concentration will reach this amount anytime in the next decade? To answer this question, obtain (and turn in) a plot the graph of the solution over a long enough time window. To do this you'll have to code in the relevant portion of the solution as a sum. Mathematica has a command “Sum”; also note that in Mathematica the base of the natural logarithm is “E” (not “e”), and the Heaviside unit step u(t) is coded as “Heaviside Thetaſt]”. a