You assume the amount of C14 is today what it was a few thousand years ago,
C14 dates have been calibrated by alternate dating methods. Today, however, c14 is greatly depleted because of fossil fuel burning. But c14 used to be in a steady state of creation vs radioactive decay and the proof is in samples dated and compared by alternative dating methods. You can read all about how tree rings are used to prove such things work and how annual layers in lake bottoms are used to prove such things work here . . . Radiocarbon Dating
Here's the graph of how the match works out:
You see, the evidence is there. You have to deny the evidence to continue to hold to your position.
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