Half of the remaining Carbon-14 then decays over the next 5730 years leaving one fourth of the original amount.
The unstable Carbon-14 is transported down to the lower atmosphere by atmospheric activity such as storms.
Levels of carbon-14 become difficult to measure and compare after about 50,000 years (between 8 and 9 half lives; where 1% of the original carbon-14 would remain undecayed).
The question should be whether or not carbon-14 can be used to date any artifacts at all? There are a few categories of artifacts that can be dated using carbon-14; however, they cannot be more 50,000 years old.
The age of the carbon in the rock is different from that of the carbon in the air and makes carbon dating data for those organisms inaccurate under the assumptions normally used for carbon dating.
This restriction extends to animals that consume seafood in their diet.