A drug follows first-order elimination kinetics. A 200 mg IV dose produces a plasma concentration of 20 mg/L at time zero. If the elimination rate constant (ke) is 0.1 per hour, what is the plasma concentration after 10 hours?

• A 10 mg/L
• B 7.36 mg/L ✓
• C 3.68 mg/L
• D 15 mg/L

Explanation

For first-order kinetics, C = C0 × e^(-kt). Here C0 = 20 mg/L, k = 0.1 per hour, t = 10 hours. So C = 20 × e^(-0.1 × 10) = 20 × e^(-1) = 20 × 0.3679 = 7.36 mg/L. Half-life = 0.693/0.1 = 6.93 hours; after 10 hours (1.44 half-lives), concentration is between 50% and 25% of C0, consistent with 7.36 mg/L.

Reference: Goodman and Gilman's The Pharmacological Basis of Therapeutics, 14th ed.

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