Which equation expresses AUC_iv in terms of Dose and Cl?

• A. AUC_iv = Dose × Cl
• B. AUC_iv = Dose
• C. AUC_iv = Cl / Dose
• D. AUC_iv = Dose / Cl

Answer: (D)

Exposure after an IV dose is governed by how much drug is given and how quickly the body clears it. For an intravenous bolus with linear kinetics, the total amount eliminated from the body over time equals the dose, and the elimination rate is Cl × C(t). If you integrate the elimination over time, you get Dose = Cl × AUC, since AUC is the integral of concentration over time. Rearranging gives AUC = Dose / Cl. This also matches the units: Dose (mg) divided by clearance (L/h) gives mg·h/L, the units of AUC.

So this expression correctly captures that higher clearance reduces exposure, while a larger dose increases exposure. The other forms would imply wrong dependencies or units.