If a semi-log plot shows a negative slope and the slope is steeper than another, what does this indicate?

If a semi-log plot shows a negative slope and the slope is steeper than another, what does this indicate?

• A. Higher half-life
• B. Lower elimination rate
• C. Higher elimination rate
• D. Larger volume of distribution

Answer: (C)

On a semi-log plot for first-order elimination, the line’s slope is the negative of the elimination rate constant k. A more negative slope means a larger k, so the drug is eliminated faster. If one curve is steeper than another, its elimination happens more quickly, indicating a higher elimination rate constant. This also means the half-life t1/2 = 0.693/k would be shorter, since a larger k shortens the time to drop by half. Among the options, the one that matches is a higher elimination rate. The other ideas don’t fit: a higher half-life would require a smaller k (slower elimination), a lower elimination rate would produce a less steep slope, and a larger volume of distribution does not determine the slope of the elimination phase on a log plot (it affects distribution dynamics, not the elimination rate constant).

On a semi-log plot for first-order elimination, the line’s slope is the negative of the elimination rate constant k. A more negative slope means a larger k, so the drug is eliminated faster. If one curve is steeper than another, its elimination happens more quickly, indicating a higher elimination rate constant. This also means the half-life t1/2 = 0.693/k would be shorter, since a larger k shortens the time to drop by half. Among the options, the one that matches is a higher elimination rate. The other ideas don’t fit: a higher half-life would require a smaller k (slower elimination), a lower elimination rate would produce a less steep slope, and a larger volume of distribution does not determine the slope of the elimination phase on a log plot (it affects distribution dynamics, not the elimination rate constant).