For k = 0.1 h−1 and tau = 12 h, what are the t1/2 and approximate time to 90% of steady state?

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Multiple Choice

For k = 0.1 h−1 and tau = 12 h, what are the t1/2 and approximate time to 90% of steady state?

Explanation:
The main idea is that the rate of elimination is first-order, so the half-life t1/2 is fixed by the elimination rate constant: t1/2 = 0.693 / k. With k = 0.1 h−1, the half-life is 0.693 / 0.1 = 6.93 h. For regular dosing, the concentration approaches steady state over several half-lives. A common rule of thumb is that about 4–5 half-lives are needed to reach ~90–95% of steady state. That gives a time of roughly 4 × 6.93 ≈ 28 h to 5 × 6.93 ≈ 34.7 h. Rounding to a convenient value, about 36 h is a reasonable estimate for 90% of steady state. So t1/2 ≈ 6.93 h and the time to 90% of steady state is about 36 h.

The main idea is that the rate of elimination is first-order, so the half-life t1/2 is fixed by the elimination rate constant: t1/2 = 0.693 / k. With k = 0.1 h−1, the half-life is 0.693 / 0.1 = 6.93 h.

For regular dosing, the concentration approaches steady state over several half-lives. A common rule of thumb is that about 4–5 half-lives are needed to reach ~90–95% of steady state. That gives a time of roughly 4 × 6.93 ≈ 28 h to 5 × 6.93 ≈ 34.7 h. Rounding to a convenient value, about 36 h is a reasonable estimate for 90% of steady state.

So t1/2 ≈ 6.93 h and the time to 90% of steady state is about 36 h.

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