The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 11 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 4 micrograms/milliliter 6 hr after dosage. Assume the concentration decreases according to the exponential decay model.
The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 11 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 4 micrograms/milliliter 6 hr after dosage. Assume the concentration decreases according to the exponential decay model.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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a) Find the value k, and write an equation for an exponential function that can be used to predict the concentration of the drug, in micrograms/milliliter, t hours after a 1000-mg dosage.
b) Estimate the concentration of the drug 4 hr after a 1000-mg dosage.
c) To relieve a fever, the concentration of the drug should go no lower than 4
mcg/mL. After how many hours will a 1000-mg dosage drop to that level?
mcg/mL. After how many hours will a 1000-mg dosage drop to that level?
Transcribed Image Text:**Drug Concentration and Exponential Decay in the Body**
The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 11 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hour after a 1000-mg dosage and 4 micrograms/milliliter 6 hours after dosage. Assume the concentration decreases according to the exponential decay model.
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This description provides a context for understanding how drug concentrations change over time in the body, an important factor in pharmacokinetics and effective medical treatment planning. The data from this specific clinical study can be used to formulate models that predict drug behavior in patients, enabling better control over dosage and timing for optimal therapeutic outcomes.
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