Carbon Dating

Carbon dating is a technique used to estimate the age of the remains of plants and animals. Living organisms continuously exchange carbon with their environment, which keeps the proportion of radioactive carbon-14 in their tissue roughly constant; once the organism dies, this exchange stops and the carbon-14 already present simply decays away. Comparing the amount of carbon-14 remaining in a sample against the amount found in living matter lets scientists estimate how long ago the organism died.

Carbon-14 decays exponentially, following the growth-and-decay model with a negative rate constant. Its decay is usually described through its half-life — the time taken for a given amount to reduce to half its original value — which for carbon-14 is approximately $5700$ years. If $m(t)$ is the mass of carbon-14 present after $t$ years and $m_0$ is the mass at $t = 0$,