## The Biology Project > Biomath > Applications > Drug Concentrations

## Drug Concentrations

 Exponential functions can be used to model the concentration of a drug in a patient's body. Suppose the concentration of Drug X in a patient's bloodstream is modeled by, C (t) = C0 e - rt, where C (t) represents the concentration at time t (in hours), C0 is the concentration of the drug in the blood immediately after injection, and r > 0 is a constant indicating the removal of the drug by the body through metabolism and/or excretion. The rate constant r has units of 1/time (1/hr). It is important to note that this model assumes that the blood concentration of the drug (C0 ) peaks immediately when the drug is injected. Using this model, try to solve the following problems: Problem 1-Find the concentration of drug in the blood at a given time after injection. Problem 2- Calculate the value of r given data on the concentration of a drug in the blood over time. Problem 3- Calculate the time it takes for the blood concentration of a drug to decrease by a given percentage. Problem 4- Calculate the initial dose of a drug that needs to be administered. Problem 5- Calculate when a second dose of a drug needs to be given. Problem 6- Determine the time it takes for the blood concentration of a drug decrease by a given percentage. Problem 7- Calculate the value of the constant r.   Next Application: Fixation of a Mutant Gene

The Biology Project > Biomath > Applications > Drug Concentrations

Credits and Citation

The Biology Project
Department of Biochemistry and Molecular Biophysics

The University of Arizona

December 2005
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