A pharmacokinetics study models the amount of a medication in a patient’s bloodstream…
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A pharmacokinetics study models the amount of a medication in a patient’s bloodstream by the equation dtdy=0.45y, where y is the amount of drug (in milligrams) present t hours after injection. At the moment of injection, 85 mg of the drug is present in the blood.
(a) Determine an explicit expression for y(t), the amount of drug in the bloodstream t hours after injection.
(b) Calculate the amount of drug present 3 hours after injection. Round your answer to the nearest milligram.
(c) Determine the time, to the nearest tenth of an hour, at which the amount of drug in the bloodstream first exceeds 500 mg. Show all work leading to your answer.