b. Anugal Lake contains 100 cubic kilometers of pure clean water. It is fed pure water by Maya River at a rate of 50 cubic kilometers per year. At time t = 0 (years), a factory near the lake is opened and immediately started dumping a pollutant into the lake at a rate of 2 cubic kilometers per year. On the other hand, water from Anugal Lake flows into Banks River at a rate that keeps the lake's water volume constant at V cubic kilometers. Let x(t) be the volume of the pollutant in the water and assume perfect mixing in the lake. Then the concentration of the pollutant is equal to c(t) ● = x(t) V Write and solve the ODE that models the amount of the pollutant in Anugal Lake. • Draw a plot of the amount of pollutant in Anugal Lake as a function of time t. You may use a software for this. Will the amount of pollutant stabilize around some constant in the long run? Suppose that a pollutant concentration of 2% (or higher) is hazardous for fish in the lake. How long will it take for the pollutant to pose danger to the fish in the lake?
b. Anugal Lake contains 100 cubic kilometers of pure clean water. It is fed pure water by Maya River at a rate of 50 cubic kilometers per year. At time t = 0 (years), a factory near the lake is opened and immediately started dumping a pollutant into the lake at a rate of 2 cubic kilometers per year. On the other hand, water from Anugal Lake flows into Banks River at a rate that keeps the lake's water volume constant at V cubic kilometers. Let x(t) be the volume of the pollutant in the water and assume perfect mixing in the lake. Then the concentration of the pollutant is equal to c(t) ● = x(t) V Write and solve the ODE that models the amount of the pollutant in Anugal Lake. • Draw a plot of the amount of pollutant in Anugal Lake as a function of time t. You may use a software for this. Will the amount of pollutant stabilize around some constant in the long run? Suppose that a pollutant concentration of 2% (or higher) is hazardous for fish in the lake. How long will it take for the pollutant to pose danger to the fish in the lake?
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:b. Anugal Lake contains 100 cubic kilometers of pure clean water. It is fed pure
water by Maya River at a rate of 50 cubic kilometers per year. At time t = 0
(years), a
, a factory near the lake is opened and immediately started dumping a
pollutant into the lake at a rate of 2 cubic kilometers per year. On the other
hand, water from Anugal Lake flows into Banks River at a rate that keeps the
lake's water volume constant at V cubic kilometers. Let x(t) be the volume of
the pollutant in the water and assume perfect mixing in the lake. Then the
concentration of the pollutant is equal to
c(t)
=
x(t)
V
Write and solve the ODE that models the amount of the
pollutant in Anugal Lake.
Draw a plot of the amount of pollutant in Anugal Lake as a
function of time t. You may use a software for this. Will the
amount of pollutant stabilize around some constant in the long
run?
• Suppose that a pollutant concentration of 2% (or higher) is
hazardous for fish in the lake. How long will it take for the
pollutant to pose danger to the fish in the lake?
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