$$Question: A pharmacologist models the concentration of a drug in the bloodstream with the function $ h(t) = t^2 - 4t + 5m $, where $ t $ is time in hours and $ m $ is a dosage parameter. If at $ t = 3 $, the concentration equals $ 10 $, what is the value of $ m $?

Mon, 04 May 2026 16:44:46 +0000

Understanding Drug Concentration: Solving for the Dosage Parameter $ m $ In pharmacokinetics, modeling drug concentration over time is essential for determining effective and safe dosages. A recent pharmacological study uses the function $ h(t) = t^2 - 4t + 5m $ to represent the concentration of a drug in the bloodstream $ t $ hours after administration. Given that at $ t = 3 $, the concentration $ h(t) $ equals 10, this article explains how to solve for the dosage parameter $ m $. ### Setting Up the Equation We are given:
$$
h(t) = t^2 - 4t + 5m
$$
and the condition:
$$
h(3) = 10
$$