Radiocarbon dating dates back
When dating wood there is no such problem because wood gets its carbon straight from the air, complete with a full dose of C-14.
The creationists who quote Kieth and Anderson never tell you this, however.
Carbon-14 is continually formed in nature by the interaction of neutrons with nitrogen-14 in the Earth’s atmosphere; the neutrons required for this reaction are produced by cosmic rays interacting with the atmosphere.
Radiocarbon present in molecules of atmospheric carbon dioxide enters the biological carbon cycle: it is absorbed from the air by green plants and then passed on to animals through the food chain.
Admittedly, this old wood comes from trees that have been dead for hundreds of years, but you don't have to have an 8,200-year-old bristlecone pine tree alive today to validly determine that sort of date.
Of course, species of tree tend to produce two or more growth rings per year.
But other species produce scarcely any extra rings.
Carbon-14 has a half-life of 5,730 ± 40 years—, half the amount of the radioisotope present at any given time will undergo spontaneous disintegration during the succeeding 5,730 years. It has proved to be a versatile technique of dating fossils and archaeological specimens from 500 to 50,000 years old.
Because carbon-14 decays at this constant rate, an estimate of the date at which an organism died can be made by measuring the amount of its residual radiocarbon. The method is widely used by Pleistocene geologists, anthropologists, archaeologists, and investigators in related fields.