Which statement is true about the half-life equation?

• A. t1/2 = Dose / AUC
• B. t1/2 = 0.693 × Vd / Cl
• C. t1/2 = Css / Rate_in
• D. t1/2 = AUC / Dose

Answer: (B)

Half-life in first-order elimination is determined by how widely a drug distributes in the body and how quickly it is cleared. The standard relationship is t1/2 = 0.693 × Vd / Cl, because the elimination rate constant k equals Cl divided by Vd, and t1/2 = ln2 / k.

This means that with a larger volume of distribution and the same clearance, the half-life lengthens; with faster clearance and the same distribution, the half-life shortens. For example, if Vd doubles while Cl stays the same, t1/2 doubles; if Cl doubles with the same Vd, t1/2 halves.

The other expressions mix dose, AUC, or steady-state concepts in ways that do not yield half-life. For instance, AUC equals Dose divided by Cl, so Dose divided by AUC equals Cl, not t1/2. At steady state during a constant infusion, Css equals Rate_in divided by Cl, which again does not give t1/2. And AUC divided by Dose equals 1/Cl, not t1/2.