What is the formula for AUC after IV dosing?

• A. AUC = Dose / Cl
• B. AUC = Cl / Dose
• C. AUC = Dose × Cl
• D. AUC = Dose / (Cl × k)

Answer: (A)

AUC after IV dosing represents total systemic exposure, and with an IV bolus there is no absorption phase, so the entire dose enters the circulation (bioavailability F = 1). The concentration–time profile follows c(t) = (Dose / Vd) e^{-kt}. Integrating from zero to infinity gives AUC = (Dose / Vd) × (1 / k) = Dose / (Vd × k). Since clearance Cl equals k × Vd, this simplifies to AUC = Dose / Cl. In other words, exposure increases with the dose and decreases with how quickly the body clears the drug, and for IV administration the formula reduces exactly to Dose divided by Clearance.