Pharmacologists model the concentration (in mg/L) of a drug in a patient’s…
MATHEMATICS · Multi-part · AP · Calculus AB · Differential Equations · Differential Equations
Problem
Pharmacologists model the concentration C(t) (in mg/L) of a drug in a patient’s bloodstream after intravenous injection by an exponential function. One hour after injection the concentration is 8 mg/L, and four hours after injection the concentration is 20 mg/L. Assume C(0)=C0 and that C′(t)=kC(t) for some constant k.
(a) Determine the values of C0 and k that satisfy the information given.
(b) Using your model, approximate the drug concentration six hours after injection.
(c) Calculate the time, to the nearest tenth of an hour, at which the concentration will reach 40 mg/L.