Small amounts of carbon-14 are not easily detected by typical Geiger–Müller (G-M) detectors; it is estimated that G-M detectors will not normally detect contamination of less than about 100,000 disintegrations per minute (0.05 µCi). This is how carbon dating works: Carbon is a naturally abundant element found in the atmosphere, in the earth, in the oceans, and in every living creature.
It takes another 5,730 for half of the remainder to decay, and then another 5,730 for half of what's left then to decay and so on.
The period of time that it takes for half of a sample to decay is called a "half-life." Radiocarbon oxidizes (that is, it combines with oxygen) and enters the biosphere through natural processes like breathing and eating.
Plants and animals naturally incorporate both the abundant C-12 isotope and the much rarer radiocarbon isotope into their tissues in about the same proportions as the two occur in the atmosphere during their lifetimes.
One rare form has atoms that are 14 times as heavy as hydrogen atoms: carbon-14, or C ratio gets smaller.
So, we have a “clock” which starts ticking the moment something dies.