About a week ago an actress that I occasionally follow on YouTube did a vlog which touched on CERN's announcement on the activity at 125 GeV and also raised a question about the movie Prometheus and how one could do radiocarbon dating on an alien planet (see 4:43-6:11 in the vlog). The process which determines the amount of Carbon-14 in the atmosphere involves more than just the rate of decay of Carbon-14. First of all the Carbon-14 is produced by the interaction of cosmic rays with Nitrogen-14 in the stratosphere. It is then oxidized to form CO2 which is removed by absorption in the oceans and by plant life through the process of photosynthesis. Excess Carbon-14 was introduced into the atmosphere by nuclear testing and monitoring has shown that CO2 is removed from the atmosphere at a faster rate than could be explained by ratioactive decay.
The decrease of Carbon-14 in the atmosphere is an example of a storage process with a relaxation time, τ, of about 16 years. The emission of CO2 by burning fossil fuels has also helped to reduce the relative amount of atmospheric Carbon-14. Radioactive decay of Carbon-14 in fossil fuels is responsible for the small fraction found in them. Burning wood can return Carbon-14 to the atmosphere.