A new drug is given orally every 12 hours and follows first-order kinetics with a half-life of 12 hours. Approximately how long will it take to reach 95% of the eventual steady-state plasma concentration?
- A 24 hours
- B 36 hours
- C 52 hours ✓
- D 120 hours
Correct answer: C. 52 hours
Explanation
With first-order elimination, the approach to steady state depends only on the half-life, not on the dose or interval. After each half-life the concentration rises by half the remaining gap: about 50% at one half-life, 75% at two, 87.5% at three, 93.75% at four, and roughly 97% at five half-lives. Five half-lives equals 60 hours here, so 52 hours (about 4.3 half-lives) gives close to 95%. Option D incorrectly multiplies the dosing interval rather than the half-life.
Reference: Katzung's Basic and Clinical Pharmacology, 16th ed.
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