The percentage of drug remaining in the plasma after 3 half life is
Starting with 100% of the drug. After one half-life, it would be 50%. After two half-lives, that's 25% (half of 50%). Then after three half-lives, it would be 12.5% (half of 25%). So the answer should be 12.5%. Let me check if that's correct. Yeah, the formula is (1/2)^n * 100%, where n is the number of half-lives. For three half-lives, (1/2)^3 = 1/8 = 12.5%.
Now, the options aren't provided, but the correct answer is 12.5%. The user probably left the options blank. The wrong options might include numbers like 50%, 25%, 6.25%, or maybe 75%. Let's think about why those are wrong. For example, 50% is after one half-life, 25% after two, 12.5% after three, and 6.25% after four. So if the options had those, the correct one is 12.5%.
The core concept here is understanding drug elimination kinetics, specifically first-order kinetics where the half-life is constant. The key point is that each half-life reduces the concentration by half, which is exponential decay. The clinical pearl here is that after 4-5 half-lives, the drug is considered to be almost completely eliminated from the body, which is important for dosing and withdrawal times.
**Core Concept**
The elimination of drugs follows first-order kinetics, where each half-life reduces the plasma concentration by 50%. After **n** half-lives, the remaining drug is calculated as **(1/2)^n Γ 100%**. This principle is critical for predicting drug clearance and dosing intervals.
**Why the Correct Answer is Right**
After 3 half-lives:
1. First half-life: 100% β 50%
2. Second half-life: 50% β 25%
3. Third half-life: 25% β 12.5%
This exponential decay reflects first-order kinetics, where the rate of elimination is proportional to the drug concentration. No enzymes or receptors are involved in this calculation, as it is purely a kinetic model.
**Why Each Wrong Option is Incorrect**
**Option A:** 50% is the remaining drug after 1 half-life.
**Option B:** 25% is the remaining drug after 2 half-lives.
**Option D:** 6.25% is the remaining drug after 4 half-lives.
**Clinical Pearl / High-Yield Fact**
Remember: **After 4β5 half-lives, 94β97% of a drug is eliminated**, which determines the time to reach steady-state or complete clearance. Use the formula **(1/2)^