You are given a fossil and told that approximately 3% of the ¹⁴C originally in the sample is still there. How old is your sample? (Note that ¹⁴C has a half-life of 5730 years). A)approximately 11,500 years B)approximately 17,000 years C)approximately 23,000 years D)approximately 29,000 years

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Quizplus · Accepted Answer

The decay of ¹⁴C (which is a stand-in for Carbon-14) follows an exponential decay model. Given that the half-life of Carbon-14 is 5730 years and only 3% of the original amount remains, we can calculate the number of half-lives that have passed. The formula to calculate the number of half-lives is: $n = \frac{\log(\text{final amount/original amount})}{\log(1/2)}$. Substituting the given values, $n = \frac{\log(0.03)}{\log(0.5)} \approx 5$. Multiplying the number of half-lives by the half-life duration: $5 \times 5730 \approx 28650$ years, which rounds to approximately 29,000 years.

You Are Given a Fossil and Told That Approximately 3