The concentration of a drug in the body decreases exponentially after a dosage is given. In...

 

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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 12 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 5 micrograms/milliliter 4 hr after dosage. Assume the concentration decreases according to the exponential decay model. 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 5 mcg/mL. After how many hours will a 1000-mg dosage drop to that level? a) k= (Round to three decimal places as needed.) The concentration of a drug in the body decreases exponentially after a dosage is given. In one clinical study, adult subjects averaged 12 micrograms/milliliter (mcg/mL) of the drug in their blood plasma 1 hr after a 1000-mg dosage and 5 micrograms/milliliter 4 hr after dosage. Assume the concentration decreases according to the exponential decay model. 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 5 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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