t = -t½/ln(2) × ln(N/N₀)
Carbon-14 is a radioactive isotope with a half-life of 5,730 years, continuously produced in the atmosphere by cosmic ray bombardment of nitrogen. Living organisms absorb C-14 through food and air, maintaining equilibrium with atmospheric levels. At death, C-14 intake stops and the isotope decays: N(t) = N₀ × e^(-λt), where λ = ln(2)/t½. By measuring the remaining C-14 ratio, we calculate time since death. At 50% remaining: ~5,730 years old. At 25%: ~11,460 years. The practical limit is about 50,000 years (~9 half-lives, 0.2% remaining). Willard Libby won the 1960 Nobel Prize for developing this technique. Modern AMS (Accelerator Mass Spectrometry) can date samples as small as 1 mg of carbon, but calibration curves are needed because atmospheric C-14 levels have varied over time due to solar activity and fossil fuel burning (Suess effect).