Simply false. There are drastic changes in the birth and death rates due to things like food availability, etc. It hardly fits your 'model'.
Exactly HOW do things like solar flares throw off the dates? I challenge you to provide a citation for this.
It's not simply false. Pick online Wikipedia references by scholars of estimates of population circa Colonial Times, the time of Jesus, etc. The math is consistent until the 20th century and the advent of geriatrics, birth control, etc.
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Decay Rate Changes:
In 2010, researchers at Purdue and Stanford published evidence that radio decay rates are not as constant as geochronologists have thought. Dating the earth through radiometric methods may therefore be even less simple than previously believed.
Dec 13, 2006, a magnificent solar flare flung radiation and solar particles toward Earth. Purdue nuclear engineer Jere Jenkins had been measuring the decay rate of manganese-54, and he noticed that a day and a half before the flare, the decay rate of Mn-54 started to drop a little. That was interesting.
Ephraim Fischbach, a physics professor at Purdue, had already found a variety of disagreements on decay rates in the literature. Fischbach had been looking for a good way to generate truly random numbers and had turned to radioactive isotopes. Chunks of radioactive elements might decay at steady rates, but the individual atoms within them decay unpredictably. Fischbach could therefore use the randomly timed ticks of a Geiger counter to generate lists of numbers.
As he did more research, though, Fischbach found variations in the published decay rates of certain isotopes. He also found that the decay rates of silicon-32 and radium-226 showed seasonal variation, according to data collected at Brookhaven National Laboratory on Long Island and the Federal Physical and Technical Institute in Germany. When the decay rate of Jenkins' Mn-54 dropped during the solar flare, Jenkins and Fischbach stood up straighter and paid attention.
"Everyone thought it must be due to experimental mistakes, because we're all brought up to believe that decay rates are constant," Peter Sturrock, Stanford professor emeritus of applied physics, commented on the issue.
There was more to the question than instrumental error. Jenkins, Fischbach and their colleagues proceeded to publish papers on the variations in radiometric decay rates in journals like
Astroparticle Physics,
Nuclear Instruments and
Methods in Physics Research. They argued that the variations were not caused by weaknesses in their detection systems, but were actual variations in the decay rates themselves.