Thank-you Steve for your explanation on how C-14 is continuously
formed and recycled.
You wondered why the C-14 method is trusted with things thought
to be in the thousands, maybe low tens of thousands of years old
but not trusted when it indicates much larger ages.
The answer is the that half-life of C-14 is relatively short
(5730 years) compared to these large ages. Due to the exponential
nature of radioactive decay, once the material has gone thru 10 -
20 half lives, the decay curve is essentially flat and
asymptotically approaching zero. Thus estimations of ages greater
than 50 -100 thousand years are inaccurate to the point of being
meaningless. Other radioactive materials with much longer
half-lives must be used to date material thought to be older than
this in order to have any hope of credible results.
Joe Reimers