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In the 70's: If this sort of thing interests you, you should find the journal Radiocarbon and read one of the issues devoted to calibration.
For example, see Radiocarbon 46,1029 (2005), which has a calibration curve that goes back 26,000 years.
It is produced in the upper atmosphere by radiation from the sun.
(Specifically, neutrons hit nitrogen-14 atoms and transmute them to carbon.) Land plants, such as trees, get their carbon from carbon dioxide in the air. The same is true of any creature that gets its carbon by eating such plants. Suppose such a creature dies, and the body is preserved.
We know (from other measurements) that the Sun hasn't fluctuated by more than 10 percent in the last million years.
However, even this small an adjustment was a bit of a shock.
On the Web, you could visit a dating laboratory, visit a dating service, read an encyclopedia entry or read a critique.
The Lake Suigetsu varve calibration was reported by ABC News and was published: Atmospheric Radiocarbon Calibration to 45,000 yr B.
So, anything more than about 50,000 years old probably can't be dated at all.In short, unless you have evidence to the contrary, you should assume that most of the carbon in a fossil is from contamination, and is not originally part of the fossil. The nuclear tests of the 1950's created a lot of C14.Also, humans are now burning large amounts of "fossil fuel".Historians don't have "right answers" for really old things.
However, carbon dating has done well on young material like the Dead Sea Scrolls, the Minoan ruins, and acacia wood from the tomb of the pharoah Zoser.Old samples contain much less C14, so the measured date of older samples is strongly affected by even small amounts of contamination.