How old is the Earth?

[Anomalocaris]

Well if the Earth is really 4.5 billion years old then you cannot "observe" that decay rates are constant because yoru observation is vastly too small and insignificant compared to the whole time period. Even if you could observe it for 100 years it would still only be 2.2X10^-11 percent of the total time. Even a curved line looks straight when you only observe an insignificant portion of it. So you're going to have to provide some other backing as to how you know those rates are constant.

Therefore a bunch of gullible desert herders who hasn't heard of the concept of "experiment", but carry around a divine box that talks to them through a hereditary priesthood, were right, and the earth is no more than 6000 years old.

Incidentally people who actually do experiments with much better boxes can directly measure forces governing decay directly over the entire 4.5 billion years in which the earth existed. By measuring the decay in the output curve and spectrum of supernova at different distances, we directly observe radio active decay behavior of very specific isotopes created during the supernova at different times in the past, and we directly constraint the behavior of nuclear strong force underlying those decays. So, yes. We've checked the decay rate over the entire 4.5 billion years, we've done 13 orders of magnitude better than your severely order-of-magnitude-befuddled 2.2 E-11 percent assessment, and found that force governing radio active decay has not changed.