Clearance is defined as the volume of plasma cleared of drug per unit time. For an intravenous dose, which equation relates AUC to dose and clearance?

• A. AUC = Dose / Cl
• B. AUC = Cl / Dose
• C. AUC = Dose × Cl
• D. AUC = Rate of elimination / plasma concentration

Answer: (A)

Clearance sets how quickly drug is removed, while AUC reflects total systemic exposure. For an IV dose, the entire injected amount eventually gets cleared, so Dose equals the total amount eliminated over time. The elimination rate at any moment is Elimination rate = Cl × C(t); integrating over time gives Dose = ∫ Elimination rate dt = Cl × ∫ C(t) dt = Cl × AUC. Rearranging yields AUC = Dose / Cl. This also matches the units: mg for dose, L/h for clearance, and mg·h/L for AUC. If the drug were given by another route with incomplete bioavailability, AUC would be (F × Dose)/Cl, but for IV administration F = 1, so AUC = Dose/Cl.