Question

A shallow reservoir has a one-square-kilometer water surface and an average (+ water depth of 4 meters. Initially it is filled with fresh water, but at time t 0 water 80 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 60- flows out at the same rate. Your first task is to find the amount x(t) of pollutant (in 40- millions of liters) in the reservoir after t months. The incoming water has a pollutant concentration of c(t) 20 liters per cubic meter (L/m). Verify that the graph of x(t) resembles the steadily rising curve shown here, which approaches asymptotically the graph of the equilibrium solution x(t) 80 that corresponds to the reservoir's long-term pollutant content. How long does it take the pollutant concentration in the reservoir to reach 16 L/m3? 20- 0+ 0 120 40 80 x(t)

Answer 1

Inilial seservoir volime 4x10 m3 Ualurme 4000 x 106 20- t be ditse of pollufaut al time t Culflow and in fous haue same rate sovume is Consl- As ifereudial equ fermed ds 2eoxtoox The di 200x1600X 4x106 dx dt Ho5) X 20 dx 20 C n4x1d 20 4x10e X orto(-e 8ox e. 3o(1-e) llion Latre

at t 20 million lise Xt)= 0(1-e 20 16L4x103 m3 GY million litre g0(1-e deloing we g-t-20 toe 32.188

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