This assumption is backed by numerous scientific studies and is relatively sound.
These long time periods are computed by measuring the ratio of daughter to parent substance in a rock and inferring an age based on this ratio.
This age is computed under the assumption that the parent substance (say, uranium) gradually decays to the daughter substance (say, lead), so the higher the ratio of lead to uranium, the older the rock must be.
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While there is no proof that the rates were different in the past than they are today, there is also no proof that they were the same.