Radiocarbon dating can be used to date
And yet we know that "radiocarbon is forming 28-37% faster than it is decaying," which means it hasn't yet reached equilibrium, which means the ratio is higher today than it was in the unobservable past.
We also know that the ratio decreased during the industrial revolution due to the dramatic increase of CO produced by factories.
This page examines some of the history of the controversy—what the Bible actually says and does not say—and the scientific evidence surrounding the age of the earth.
Archbishop Ussher took the genealogies of Genesis, assuming they were complete, and calculated all the years to arrive at a date for the creation of the earth on Sunday, October 23, 4004 B. Of course, even assuming the method was valid, such an exact date is not possible from the genealogies of the Bible (Ussher assumed all the years the patriarchs lived were exactly 365.25 days long and that they all died the day before their next birthday).
C-14 is produced in the upper atmosphere when nitrogen-14 (N-14) is altered through the effects of cosmic radiation bombardment (a proton is displaced by a neutron effectively changing the nitrogen atom into a carbon isotope).
The new isotope is called "radiocarbon" because it is radioactive, though it is not dangerous.
This man-made fluctuation wasn't a natural occurrence, but it demonstrates the fact that fluctuation is possible and that a period of natural upheaval upon the earth could greatly affect the ratio.
Volcanoes spew out CO which could just as effectively decrease the ratio.