10
advanced-math

Carbon-14 has a half-life of 5,730 years. If a fossil has 25% of its original carbon-14, approximately how old is it?

A

11,460 years

B

5,730 years

C

17,190 years

D

2,865 years

Correct Answer: A

Choice A is the correct answer. Work backwards from the remaining percentage.

  1. Remaining: 25% = 14\frac{1}{4} of original.
  2. Half-lives: 14=(12)2\frac{1}{4} = (\frac{1}{2})^2, so 2 half-lives have passed.
  3. Time: 2×5730=11,4602 \times 5730 = 11,460 years.
  4. Formula: 0.25=(0.5)t/57300.25 = (0.5)^{t/5730}, solving gives t=11,460t = 11,460.

💡 Strategic Tip: 25% = 14\frac{1}{4} = 2 half-lives have occurred.

Choice B is incorrect because this is only 1 half-life (50% remaining). Choice C is incorrect because this is 3 half-lives (12.5% remaining). Choice D is incorrect because this is half of one half-life.