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The project is meant to create an equation that can be used to estimate the amount of organic pollutant – bacteria - that is present in a swimming pool per day from rainwater. This equation is derived through a differential equation of the rate in minus the rate out. The created differential equation is an ordinary linear differential equation and is solved using an integration factor. The general solution is then converted into a specific equation using an initial condition. The resulting equation provides an approximate number of organic contaminants x(t) present in the pool after an amount of time in days (t). The equation finds that the pool – during its closure – has been cleaned often enough. It also provides a method to estimate the amount of contamination from rain after any other extended closures.

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Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License.

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Mathematics Commons




Arcadii Grinshpan, Mathematics and Statistics

Robert Powell, Environ

Problem Suggested By:

Robert Powell