A dose of a certain medication is injected into a patient
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A dose of a certain medication is injected into a patient. The concentration C(t) of the medication in the bloodstream, measured in milligrams per liter (mg/L), satisfies dtdC=kC, where t is the time in hours since the injection. At the moment of injection (t=0) the concentration is 120 mg/L. Three hours later, the concentration has fallen to 90 mg/L.
(a) Formulate the differential equation that models the concentration, clearly indicating the meaning of the constant k and any initial condition(s).
(b) Determine the value of k (including units) that is consistent with the given data.
(c) Using your value of k, calculate the concentration of the medication eight hours after the injection.
(d) The medication is considered medically effective until its concentration drops to 30 mg/L. Estimate the time, to the nearest tenth of an hour, at which the medication ceases to be effective.