10
advanced-math

Iodine-131 has a half-life of 8 days. A hospital receives 200 grams. How much will remain after 32 days?

A

12.5 grams

B

25 grams

C

6.25 grams

D

50 grams

Correct Answer: A

Choice A is the correct answer. Calculate using half-lives.

  1. Half-lives: 328=4\frac{32}{8} = 4 half-lives.
  2. Remaining: 200×(12)4=200×116=12.5200 \times (\frac{1}{2})^4 = 200 \times \frac{1}{16} = 12.5 grams.
  3. Formula: A(t)=200(0.5)t/8A(t) = 200(0.5)^{t/8}.

💡 Strategic Tip: 4 half-lives means 116\frac{1}{16} of original remains.

Choice B is incorrect because this is after 3 half-lives (24 days). Choice C is incorrect because this would be after 5 half-lives (40 days). Choice D is incorrect because this is after 2 half-lives (16 days).