The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 14 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 3 micrograms/milliliter 4 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 3 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?
k = ________(Round to three decimal places as needed.)

Question

03-08-2021
Mathematics

Answered

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The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 14 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 3 micrograms/milliliter 4 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 3 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?
k = ________(Round to three decimal places as needed.)

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