By the way, C-14 in the atmosphere does not come from CO2. It comes from Nitrogen absorbing a neutron.
Radiocarbon Dating and Bomb Carbon - Beta Analytic
So let's say CO2 doubles, Nitrogen is unchanged and the creation rate of C-14 is the same.
By volume, dry air contains 78.09% nitrogen, 20.95% oxygen,[1] 0.93% argon, 0.04% carbon dioxide,
Atmosphere of Earth - Wikipedia
C14 is a radioactive isotope of carbon, which is normally C12, which means it's the carbon atom that picked up two extra neutrons making the atomic mass unstable. It is not because of a nitrogen atom picking up an extra neutron or two.
If the volume of CO2 increases in the earth's atmospheric content it's most likely due to a decrease in free O2.
The nuclear tests conducted in the last century, especially those above ground, increased the content of C14 in the atmosphere also without significantly increasing the CO2 content of the atmosphere.
If the carbon dioxide in the atmospheric content was double say ten thousand years ago for a few centuries. Yet assume for testing purposes that it remains constant throughout the past and the piece we're testing. Then it would throw off the radiocarbon dating process because we didn't account for the excess C14 that would be in the testing because it would be double the expected amount.
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