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 contaminated with a liquid pollutant begins flowing into the reservoir at the rate of 500 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 a pollutant concentration of ​c(t)=2020 liters per cubic meter ​(L/m cubedm3​). 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 1616 ​L/m cubedm3​?

Answer 1

Tnitial esemir volama enx 4m X millien 11 Lifres 4croo million itres volume Let xbe the lite pollutant at fmet A bud flare ond in tloto have same Vlume ae, ic cnutant The differcen tiol esn form dx 4X 106 da In tegpa ting 8-kn1.01X16-2 +C ts K 1.01 XI0-12 8-08X00 ter 4t te0, 8:08 X109 C 1-e

For concentation, B/1 9191 1616 x 4 XI06 L 6464 X(o6 Cabe Hhutng 6464 x106 873 1- 6.46 e O 2 8D8 -6094 ln 0.2 17 1287 17 Aays So, it would talee fo rerch 12 momt amd 26 concen fratin 1616 L