The concentration of a medication in a patient’s bloodstream is measured in…
MATHEMATICS · Multi-part · A Level · Mathematics · Quantities and units in mechanics · Quantities and units in mechanics
Problem
The concentration C(h) of a medication in a patient’s bloodstream is measured in milligrams per liter (mg/L), where h is the number of hours since the medication was administered.
At h=2, clinicians find that C′(2)=−0.75mg/(L⋅hr).
(a) Convert the value of C′(2) to units of mg/(L·min). Show every unit conversion step symbolically before obtaining a decimal result.
(b) Interpret the meaning of your converted value in the context of the medication’s effectiveness. Your answer should be a complete sentence that references both magnitude and units.
(c) Assuming C′(h) remains constant at the value found in part (a) for the next 15 minutes, estimate the change in concentration over that interval. State your answer with appropriate units and justify your reasoning.