A patient receives an intravenous dose of Drug A at time
MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
A patient receives an intravenous dose of Drug A at time t=0. The concentration of Drug A in the bloodstream (in mg/L) decays according to A(t)=80e−0.090t for 0≤t<4, where t is measured in hours. Simultaneously, the body converts Drug A into an active metabolite, Drug B, whose concentration rises according to B(t)=10e0.110t over the same time interval.
(a) Determine the time, to the nearest hundredth of an hour, at which the concentrations of Drug A and Drug B are equal.
(b) Compute A′(t) and B′(t) at the time found in part (a). Which drug’s concentration is changing more rapidly at that instant?
(c) Immediately after 4 hours, another identical dose of Drug A is administered, resetting its concentration to 80 mg/L while Drug B continues to follow its existing model. Explain whether Drug B can exceed Drug A in concentration at any time before the second dose, supporting your argument with quantitative reasoning.