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 3 micrograms/milliter 5 hr after dosage. 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?
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 3 micrograms/milliter 5 hr after dosage. 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?
Chapter6: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 29PT: A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days,...
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Transcribed Image Text: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 3
micrograms/milliter 5 hr after dosage.
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?
a) k=
(Round to three decimal places as needed.)
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