Problems deal with a shallow reservoir that has a one square kilometer water surface and an average water depth of 2 meters. Initially it is filled with fresh water, bit at time t = 0 water contaminated with a liquid pollutant begins flowing into the reservoir at the rate of 200 thousand cubic meters per month. The well-mixed water in the reservoir flows out at the same rate. Your first task is to find the amount x(t) of pollutant (in millions of liters) in the reservoir after t months.
The incoming water has pollutant concentration c(t) = 10(1 + cos t) L/m3 that varies between 0 and 20, with an average concentration of 10 L/m3 and a period of oscillation of slightly over months. Does it seem predictable that the lake’s polutant content should ultimately oscillate periodically about an average level of 20 million liters?
Verify that the graph of x(t) does, indeed, resemble the oscillatory curve shown in Fig. How long does it take the pollutant concentration in the reservoir to reach 5 L/m3?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.