The method of carbon dating makes use of the fact that all living organisms contain two isotopes of carbon, carbon-12, denoted 12C (a stable isotope), and carbon-14, denoted 14C (a radioactive isotope).
The amount of Carbon 14 contained in a preserved plant is modeled by the equation $$ f(t) = 10e^.
The carbon-14 isotope would vanish from Earth's atmosphere in less than a million years were it not for the constant influx of cosmic rays interacting with molecules of nitrogen (N) into organic compounds during photosynthesis, the resulting fraction of the isotope 14C in the plant tissue will match the fraction of the isotope in the atmosphere.
After plants die or are consumed by other organisms, the incorporation of all carbon isotopes, including 14C, stops.
When an organism dies, the amount of 12C present remains unchanged, but the 14C decays at a rate proportional to the amount present with a half-life of approximately 5700 years.
This change in the amount of 14C relative to the amount of 12C makes it possible to estimate the time at which the organism lived.