Two aquariums contain 10 liters of water each. Initially, the first aquarium contains no oxygen, but...

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Two aquariums contain 10 liters of water each. Initially, the first aquarium contains no oxygen, but has a plant that produces oxygen at a rate of 0.1 mg/hour. The second aquarium initially has 0.3 mg of oxygen and contains a fish that consumes 0.2 mg of oxygen per hour. Each pipe connecting the aquariums transfers the oxygen-water mixture between aquariums at a rate of 10 liters/hour. 1. (4.5 pts) Model the problem using a system of differential equations. Let x(t) be milligrams of oxygen in the aquarium that contains the plant, and y(t) be milligrams of oxygen in the aquarium that contains the fish. 2. (1 pt) What are suitable assumptions and limitations on the mathematical model? 3. (1.5 pts) Identify initial conditions of of r(t) and y(t). 4. (6 pts) Use an analytical method to solve the system of differential equations. 5. (3 pts) Use an analytical method to find how long it will take oxygen levels in tanks to be the same. Two aquariums contain 10 liters of water each. Initially, the first aquarium contains no oxygen, but has a plant that produces oxygen at a rate of 0.1 mg/hour. The second aquarium initially has 0.3 mg of oxygen and contains a fish that consumes 0.2 mg of oxygen per hour. Each pipe connecting the aquariums transfers the oxygen-water mixture between aquariums at a rate of 10 liters/hour. 1. (4.5 pts) Model the problem using a system of differential equations. Let x(t) be milligrams of oxygen in the aquarium that contains the plant, and y(t) be milligrams of oxygen in the aquarium that contains the fish. 2. (1 pt) What are suitable assumptions and limitations on the mathematical model? 3. (1.5 pts) Identify initial conditions of of r(t) and y(t). 4. (6 pts) Use an analytical method to solve the system of differential equations. 5. (3 pts) Use an analytical method to find how long it will take oxygen levels in tanks to be the same.

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1 Let xt be the milligrams of oxygen in the aquarium that contains the plant and yt be the milligrams of oxygen in the aquarium that contains the fish ... View the full answer