Approximately how many half-life periods are required for a serum drug concentration to reach 97-99% of the steady state?

Approximately how many half-life periods are required for a serum drug concentration to reach 97-99% of the steady state?

• A. 1-3
• B. 2-4
• C. 5-7
• D. 7-9

Answer: (C)

The main idea is that with repeated dosing, serum concentrations approach steady state in a predictable way: after each half-life, the gap to steady state halves. The fraction of steady state reached after n half-lives is 1 − (1/2)^n. Compute a few: after 5 half-lives, you’re at about 96.9%; after 6, about 98.4%; after 7, about 99.2%. Since 97–99% falls in this range, roughly 5–7 half-lives are needed to reach that level. So the best answer is about 5–7 half-lives.

The main idea is that with repeated dosing, serum concentrations approach steady state in a predictable way: after each half-life, the gap to steady state halves. The fraction of steady state reached after n half-lives is 1 − (1/2)^n.

Compute a few: after 5 half-lives, you’re at about 96.9%; after 6, about 98.4%; after 7, about 99.2%. Since 97–99% falls in this range, roughly 5–7 half-lives are needed to reach that level.

So the best answer is about 5–7 half-lives.