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.
The older an organism's remains are, the less beta radiation it emits because its C-14 is steadily dwindling at a predictable rate.
Question: A sample that is more than fifty thousand years old shouldn't have any measurable C-14. Radiocarbon dating doesn't work well on objects much older than twenty thousand years, because such objects have so little C-14 left that their beta radiation is swamped out by the background radiation of cosmic rays and potassium-40 (K-40) decay. this isotope [K-40] accounts for a large part of the normal background radiation that can be detected on the earth's surface" (p. This radiation cannot be totally eliminated from the laboratory, so one could probably get a "radiocarbon" date of fifty thousand years from a pure carbon-free piece of tin.
Radiocarbon dating can easily establish that humans have been on the earth for over twenty thousand years, at least twice as long as creationists are willing to allow.
Therefore it should come as no surprise that creationists at the Institute for Creation Research (ICR) have been trying desperately to discredit this method for years.
ICR creationists claim that this discredits C-14 dating. Answer: It does discredit the C-14 dating of freshwater mussels, but that's about all.
Kieth and Anderson show considerable evidence that the mussels acquired much of their carbon from the limestone of the waters they lived in and from some very old humus as well.