Radioactive carbon dating works because the amount of carbon-14 is constant while the organism is living and once the organism dies the amount of carbon-14

Once the organism dies the amount of carbon-14 decreases exponentially.

The exponential, radioactive decay of carbon 14 is used to estimate the death dates of organic material.

Living organisms have approximately the same ratio of C12 to C14 in their tissues. Once the organism dies C14 decays into nitrogen 14. Decay of C14 to nitrogen 14 changes the ratio of C12 to C14. The ratio of C12 to C14 in dead material can be compared to the ratio when the organism was alive to estimate the date of its death. Radiocarbon dating can be used on different samples such as bone, cloth, wood and plant fibers.