Amount of drug left after four plasma half–lives is:
Now, for the core concept: This is about pharmacokinetics, specifically elimination half-life. The half-life is the time it takes for the plasma concentration to reduce by half. Each subsequent half-life continues this pattern.
Why is the correct answer right? Because each half-life halves the remaining drug. So starting with 100%, after one half-life it's 50%, then 25%, 12.5%, and finally 6.25% after four. That's straightforward exponential decay.
For the wrong options: If the options were, say, 25%, 12.5%, or 50%, those would be incorrect because they don't account for four half-lives. For example, 25% is after two half-lives, 12.5% after three, and 50% after one. So any of those would be wrong here.
Clinical pearl: Remember that after 4-5 half-lives, a drug is considered to be almost completely eliminated from the body. This is important for dosing intervals and understanding drug clearance. The 6.25% remaining after four half-lives is a key point in determining when a drug is out of the system.
Putting it all together, the correct answer is 6.25%, which is option C.
**Core Concept**
Drug elimination follows first-order kinetics, where the plasma concentration decreases by half every half-life. After each half-life, the remaining drug quantity is halved exponentially. This principle is critical in determining dosing intervals and predicting drug clearance.
**Why the Correct Answer is Right**
After one half-life, 50% remains; after two, 25%; three, 12.5%; and four, **6.25%**. This exponential decay is calculated as **(1/2)^n × 100**, where **n** is the number of half-lives. Four half-lives reduce the drug to **6.25%** of the initial dose, aligning with the formula for first-order elimination.
**Why Each Wrong Option is Incorrect**
**Option A:** Likely represents 12.5% (three half-lives). Incorrect as it skips the fourth halving.
**Option B:** Likely 25% (two half-lives). Fails to account for full four half-lives.
**Option D:** Likely 50% (one half-life). Grossly overestimates remaining drug.
**Clinical Pearl / High-Yield Fact**
Drugs are considered **~94% eliminated** after four half-lives