How do you calculate the elimination half-life from the terminal slope of a concentration-time curve?

• A. t1/2 = ln(2) / λz
• B. t1/2 = λz / ln(2)
• C. t1/2 = 2 × λz
• D. t1/2 = 1 / λz

Answer: (A)

For drugs that follow first-order elimination, the concentration declines exponentially over time, so the terminal portion of a semilog concentration–time plot has a slope of −λz, where λz is the elimination rate constant. The half-life is the time it takes for the concentration to drop to half of its initial value.

Start from the first-order equation: C = C0 e^(−λz t). If the concentration is halved, C = C0/2, giving e^(−λz t1/2) = 1/2. Taking natural logs: −λz t1/2 = ln(1/2) = −ln 2. Solve for t1/2: t1/2 = ln 2 / λz.

This is why the half-life equals the natural log of 2 divided by the elimination rate constant. The other forms don’t fit because they either invert the relationship, omit the ln 2 factor, or represent a different time constant (the time for a 1/e decline) rather than a 1/2 decline.