One of the most frequent uses of radiocarbon dating is to estimate the age of organic remains from archaeological sites. When plants fix atmospheric carbon dioxide (CO2) into organic material during photosynthesis they incorporate a quantity of 14C that approximately matches the level of this isotope in the atmosphere (a small difference occurs because of isotope fractionation, but this is corrected after laboratory analysis). After plants die or they are consumed by other organisms (for example, by humans or other animals) the 14C fraction of this organic material declines at a fixed exponential rate due to the radioactive decay of 14C. Comparing the remaining 14C fraction of a sample to that expected from atmospheric 14C allows the age of the sample to be estimated. Find the differential equation that describes this situation. How would you estimate the age of a dinosaur skeleton?
- Derivatives of exponential function (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 131)