For a drug with a half-life of 12 hours, after 12 hours the concentration is at what fraction of the initial level?

For a drug with a half-life of 12 hours, after 12 hours the concentration is at what fraction of the initial level?

• A. 50%
• B. 25%
• C. 12.5%
• D. 75%

Answer: (A)

Half-life is the time required for a drug’s concentration to fall to half of its current value. The concentration after time t is C = C0 × (1/2)^(t/t1/2). Here, t equals one half-life (12 hours), so t/t1/2 = 1 and the concentration becomes C0 × 1/2 = 0.5 C0. That means it’s 50% of the initial level after 12 hours. After two half-lives (24 hours) it would be 25% of the initial, and after three half-lives (36 hours) it would be 12.5%.

Half-life is the time required for a drug’s concentration to fall to half of its current value. The concentration after time t is C = C0 × (1/2)^(t/t1/2). Here, t equals one half-life (12 hours), so t/t1/2 = 1 and the concentration becomes C0 × 1/2 = 0.5 C0. That means it’s 50% of the initial level after 12 hours. After two half-lives (24 hours) it would be 25% of the initial, and after three half-lives (36 hours) it would be 12.5%.