A shallow reservoir has a one-square-kilometer water surface and an average water depth of 2 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 400 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) = 20 liters per cubic meter (L/m³). 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) = 40 that corresponds to the reservoir's long-term pollutant content. How long does it take the pollutant content in the reservoir to reach 10 million liters? x(t) =
A shallow reservoir has a one-square-kilometer water surface and an average water depth of 2 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 400 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) = 20 liters per cubic meter (L/m³). 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) = 40 that corresponds to the reservoir's long-term pollutant content. How long does it take the pollutant content in the reservoir to reach 10 million liters? x(t) =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A shallow reservoir has a one-square-kilometer water surface and an average water depth of 2 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 400 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) = 20 liters per cubic meter
(L/m³). 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) = 40 that corresponds to the reservoir's long-term
pollutant content. How long does it take the pollutant content in the reservoir to reach 10 million liters?
x(t) =
40-
30-
20-
10-
0
10
20
t
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