A wooden relic shows a carbon-14 activity equal to 60% of that of living wood. Taking the half-life of ^14C as 5730 years and using exact logarithms, its age in years, to the nearest integer, is

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A wooden relic shows a carbon-14 activity equal to $60%$ of that of living wood. Taking the half-life of $X_{14} X_{2}^{214} C$ as $5730$ years and using exact logarithms, its age in years, to the nearest integer, is

Numerical answer type, answer in years, tolerance 15.

t = t_{1/2} lo g_{2} (A_{0} / A) = 5730 \times lo g_{2} (1/0.60) = 5730 \times 0.737 = 4223

years.