Measurement of radiocarbon was originally done by beta-counting devices, which counted the amount of beta radiation emitted by decaying atoms in the sample and not just the few that happen to decay during the measurements; it can therefore be used with much smaller samples (as small as individual plant seeds), and gives results much more quickly.The development of radiocarbon dating has had a profound impact on archaeology.
Additional complications come from the burning of fossil fuels such as coal and oil, and from the above-ground nuclear tests done in the 1950s and 1960s.
Because the time it takes to convert biological materials to fossil fuels is substantially longer than the time it takes for its in the atmosphere, which attained a maximum in 1963 of almost twice what it had been before the testing began.
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.
The older a sample is, the less (the period of time after which half of a given sample will have decayed) is about 5,730 years, the oldest dates that can be reliably measured by this process date to around 50,000 years ago, although special preparation methods occasionally permit accurate analysis of older samples.
$$ 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.