2. An industrial pond having volume 100 m is full of pure water. Contaminated water containing...

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2. An industrial pond having volume 100 m³ is full of pure water. Contaminated water containing a toxic chemical of concentration 0.0002 kg per m³ is then is pumped into the pond with a volumetric flow rate of 0.5 m³ 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). 3. In the preceding problem, change the flow rate out of the pond to 0.6 m³ per minute. How long will it take the pond to empty? Write, but do not solve, the revised initial value problem. 2. An industrial pond having volume 100 m³ is full of pure water. Contaminated water containing a toxic chemical of concentration 0.0002 kg per m³ is then is pumped into the pond with a volumetric flow rate of 0.5 m³ 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). 3. In the preceding problem, change the flow rate out of the pond to 0.6 m³ per minute. How long will it take the pond to empty? Write, but do not solve, the revised initial value problem.