The two solutions provided differ slightly in their approach in this regard.
Another approach to describing reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value.
$$ So either the answer is that ridiculously big number (9.17e7) or 30,476 years, being calculated with the equation I provided and the first equation in your answer, respectively.
Carbon has two stable, nonradioactive isotopes: carbon-12 (12C) and carbon-13 (13C).
The radiocarbon dating method is based on the fact that radiocarbon is constantly being created in the atmosphere by the interaction of cosmic rays with atmospheric nitrogen.
The resulting radiocarbon combines with atmospheric oxygen to form radioactive carbon dioxide, which is incorporated into plants by photosynthesis; animals then acquire in a sample from a dead plant or animal such as a piece of wood or a fragment of bone provides information that can be used to calculate when the animal or plant died.
Research has been ongoing since the 1960s to determine what the proportion of in the atmosphere has been over the past fifty thousand years.
The resulting data, in the form of a calibration curve, is now used to convert a given measurement of radiocarbon in a sample into an estimate of the sample's calendar age.