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Creationists assume, usually on the basis of a "flood" argument, that there have been large changes in the amount of carbon dioxide in the atmosphere during the past several thousand years. There probably have been small fluctuations, leading to an uncertainty of plus or minus ten percent, confirmed by dating objects of a known age. However, the evidence does not support the creationist claim of large changes in the amount of carbon dioxide.
The creationist argument that the ratio of C-14 to C-12 is not constant is actually based on the assumption of a young earth with an age of 10,000 years, and sudden changes in the amount of carbon dioxide in the atmosphere caused by the assumed catastrophic events of the Genesis flood. This is the motivation behind the 30,000 year figure quoted in the creationist position.
Creationists attack all radioactive dating with the claim that radioactive decay rates may have been different in the past. There is absolutely no valid evidence to support this claim. It is entirely at odds with everything that is known about nuclear physics."