5
advanced-math

A medication has a half-life of 6 hours in the bloodstream. If 400 mg is initially taken, how much remains after 18 hours?

A

50 mg

B

100 mg

C

25 mg

D

200 mg

Correct Answer: A

Choice A is the correct answer. Calculate using half-life periods.

  1. Half-lives: 186=3\frac{18}{6} = 3 half-lives.
  2. After each half-life: Multiply by 0.5.
  3. After 3 half-lives: 400×(0.5)3=400×0.125=50400 \times (0.5)^3 = 400 \times 0.125 = 50 mg.
  4. Formula: A(t)=400(0.5)t/6A(t) = 400(0.5)^{t/6}.

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

Choice B is incorrect because this is after 2 half-lives (12 hours). Choice C is incorrect because this would be after 4 half-lives (24 hours). Choice D is incorrect because this is after only 1 half-life (6 hours).