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advanced-math

Plutonium-238 has a half-life of 88 years. If 200 grams decay to 25 grams, how much time has passed?

A

264 years

B

176 years

C

88 years

D

352 years

Correct Answer: A

Choice A is the correct answer. Determine the number of half-lives.

  1. Remaining: 25200=18=(12)3\frac{25}{200} = \frac{1}{8} = (\frac{1}{2})^3.
  2. Half-lives: 3 half-lives have occurred.
  3. Time: 3×88=2643 \times 88 = 264 years.

💡 Strategic Tip:18\frac{1}{8} means 3 halvings: 50%25%12.5%50\% \to 25\% \to 12.5\%.

Choice B is incorrect because this is 2 half-lives (would leave 50 grams). Choice C is incorrect because this is 1 half-life (would leave 100 grams). Choice D is incorrect because this is 4 half-lives (would leave 12.5 grams).