Final answer:
The function M(t) = 40e −0.223t represents the concentration of a drug (oxycontin) in the bloodstream over time, with t representing hours post-administration. It illustrates the pharmacokinetics of drug decay and is based on the concept of half-life. Substituting a value for time t into the function allows calculation of the remaining drug concentration.
Step-by-step explanation:
The question involves the function M(t) = 40e −0.223t, which models the decay of a drug in a person's bloodstream over time. This is a common type of function used in the study of pharmacokinetics, a branch of pharmacology dedicated to determining the fate of substances administered to a living organism. The variables in the function include t, which represents time in hours, and M(t), which represents the number of milligrams of the drug remaining in the bloodstream at time t.
To use this function, we can substitute a specific value for t and calculate M(t) to find the remaining drug concentration at that time. This function also incorporates the concept of a half-life, which is the time it takes for half of the drug to be eliminated from the body. In pharmacology, understanding the half-life of a drug helps in determining the dosing intervals and the duration of treatment. The decay constant in this equation is specific to oxycontin, and it will vary for different substances based on their chemical properties and the body's metabolism.