Which equation correctly gives the half-life in a one-compartment model with first-order elimination?

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Multiple Choice

Which equation correctly gives the half-life in a one-compartment model with first-order elimination?

Explanation:
In a one-compartment model with first-order elimination, the elimination rate constant is k = Cl / Vd. The half-life is t1/2 = ln(2) / k, and since ln(2) ≈ 0.693, you get t1/2 = 0.693 / (Cl / Vd) = 0.693 × Vd / Cl. This shows that a larger volume of distribution lengthens the half-life (drug is more widely distributed and takes longer to reach elimination), while higher clearance shortens the half-life (elimination is faster). The correct form places Vd in the numerator and Cl in the denominator, with the 0.693 factor. The other forms would imply the opposite relationships or use an incorrect factor, which would misrepresent how Vd and Cl influence t1/2.

In a one-compartment model with first-order elimination, the elimination rate constant is k = Cl / Vd. The half-life is t1/2 = ln(2) / k, and since ln(2) ≈ 0.693, you get t1/2 = 0.693 / (Cl / Vd) = 0.693 × Vd / Cl.

This shows that a larger volume of distribution lengthens the half-life (drug is more widely distributed and takes longer to reach elimination), while higher clearance shortens the half-life (elimination is faster). The correct form places Vd in the numerator and Cl in the denominator, with the 0.693 factor.

The other forms would imply the opposite relationships or use an incorrect factor, which would misrepresent how Vd and Cl influence t1/2.

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