The half-life of carbon-14 is 5730 years. How long will it take for 7/8 of a sample of carbon-14 to decay?

If 7/8 decays, then 1/8 remains. Each half-life halves the remaining amount: after three half-lives, 1 → 1/2 → 1/4 → 1/8. Three half-lives take 3 × 5,730 = 17,190 years, so the answer is 17,190 years.

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