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The careful monitoring of a drug’s concentration in the body of a patient is of the utmost importance in modern medicine. Many of the lifesaving medications that are administered in an emergency medicine environment have a narrow window of efficacy. This effective concentration is in an ever-changing state, as the body processes and eliminates exogenous compounds that are introduced to maintain homeostasis. To ensure the proper treatment and/or management of ailments, special attention must be given to the concentration of a given drug in the body as time progresses. These changing concentrations can be evaluated and tracked using the mathematical tools that are taught in Calculus-themed courses.

In this paper, the steps required to accurately calculate the concentration of a given drug in a patient’s body will be examined. We will arrive at a formula that can reliably be used to determine this concentration at a point in time.

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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

Larry Land, Advent Health Hospital System

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Larry Land