What does the constant decay rate has to do with the age of the earth? What if the decay rate change, then what happen?
If decay rates changed, it would cause the radiometric dating methods that tell us about great ages to be wrong. If radioactive decay rates sped up the ages we would get would be older than the real age. If the Earth is really around 10,000 years old that would require speeding up radioactive decay rates so much that the Earth would melt and everyone would be fricaseed by the heat. And the radiation would fry 'em too.
Another fact is that there are many different ways that radioactive elements decay. If our methods give us the wrong answers than all those differnt ways would have to change in just the right way in a coordianted manner. Otherwise dating methods based on different modes of decay wouldn't agree so often.