7
advanced-math

A drug has a half-life of 4 hours. A patient takes 600 mg. How much remains after 12 hours?

A

75 mg

B

150 mg

C

300 mg

D

37.5 mg

Correct Answer: A

Choice A is the correct answer. Use half-life calculation.

  1. Half-lives: 124=3\frac{12}{4} = 3 half-lives.
  2. Remaining: 600×(12)3=600×18=75600 \times (\frac{1}{2})^3 = 600 \times \frac{1}{8} = 75 mg.
  3. Formula: A(t)=600(0.5)t/4A(t) = 600(0.5)^{t/4}.

💡 Strategic Tip: 3 half-lives = 18\frac{1}{8} of original amount.

Choice B is incorrect because this is after 2 half-lives (8 hours). Choice C is incorrect because this is after 1 half-life (4 hours). Choice D is incorrect because this would be after 4 half-lives (16 hours).