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As time progressed each would begin to acquire its slower modern-day stable half-life, but would they all acquire these stable rates in a uniformity which would keep them all in synchrony? If they did, all would give the same ages, you are right.
Each would probably arrive at equilibrium at different times.
As far as your comments that 16,000 years is older than when God created the earth, we know that there is more carbon in the atmosphere than there was a thousand years ago. It is somewhat accurate back to a few thousand years, but carbon dating is not accurate past this. However, this does not mean that the earth is 30 thousand years old. Because of the earths declining magnetic field, more radiation (which forms C14) is allowed into the earths atmosphere.
So a date of 9,000 or 16,000 years is more likely to be less. Carbon dating is a good dating tool for some things that we know the relative date of. Willard Libby (December 17, 1908 September 8, 1980) and his colleagues discovered the technique of radiocarbon dating in 1949.
Libbey knew that atmospheric carbon would reach equilibrium in 30,000 years.
Because he assumed that the earth was millions of years old, he believed it was already at equilibrium.
They should not change the facts to fit the theory.( "Radioisotopes and the age of the earth" pg vii) To know if carbon dating is accurate, we would have to know how much carbon was in the atmosphere in the beginning, and also how long it has been increasing, or decreasing. It's like trying to figure out how long a candle has been burning, without knowing the rate at which it burns, or its original size.See my commentary on Genesis 3 verse 17 "..cursed is the ground for your sake" When this happened there was a burst of radioactity that made the rocks appear older than they were.When each of these elements, uranium, potassium, radium etc.were switched on, it would only be natural for them to behave according to their individual properties, eventually acquiring stable half-lives of decay, at different rates.