Ok, let’s do some assumption based calculations. The assumption is this: a long long time ago, there was hardly any C14 in the atmosphere, because the earth was very well protected against cosmic radiation. Now all of a sudden this protection got removed, so cosmic radiation starts to produce C14 at a constant rate. The earth “consumes” C14 from the atmosphere. Well, plants do, by photosynthesis…
If plants would consume 1% of C14 in the atmosphere every year, then how long will it take before a balance is reached? In other words, if we would have this event at 3000 BC, when would C14 in the atmosphere reach todays concentration? And what would be the apparent C14 age in that case? This image shows a result (click to enlarge):
So it would take about 500 years, resulting in 2500 BC.
This would be the curve if the consumption is 0.5% (about 750 years, resulting in 2250 BC):
And this is for 0.3%: (about 1250 years, resulting in 1750 BC):
And this is for 0.1% (about 3500 years, resulting in 500 AC):