(Pollution) An industrial pond having volume 100m^(3) is full of pure water. Contaminated water containing a toxic chemical of concentration 0.0002 kg per m^(3) is then is pumped into the pond with a volumetric flow rate of 0.5m^(3) per minute. The contents are well-mixed and pumped out at the same flow rate. Write an initial value problem for the

Question

(Pollution) An industrial pond having volume

100m^(3)

is full of pure water. Contaminated water containing a toxic chemical of concentration 0.0002 kg per

m^(3)

is then is pumped into the pond with a volumetric flow rate of

0.5m^(3)

per minute. The contents are well-mixed and pumped out at the same flow rate. Write an initial value problem for the contaminant concentration

C(t)

in the pond at any time

t

. Determine the equilibrium concentration and its stability. Find a formula for the concentration

C(t)

. In the preceding problem, change the flow rate out of the pond to

0.6m^(3)

per minute. How long will it take the pond to empty? Write, but do not solve, the revised initial value problem.

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