As for the Earth, I'd say light radionuclides such as carbon-14 are more or less in equilibrium (as many are created by cosmic rays as many decay), and so are heavy short-lived radionuclides such as radon (as many are created by uranium and thorium decaying as many decay themselves), whereas heavy long-lived radionuclides (uranium and thorium) decay with nothing replenishing them. So the total radioactivity is decreasing (at least on timescales long compared with the 2x11-year solar cycle but short compared with the Earth's age).
When an uranium atom splits, a chain begins. Where more energy is released later in this chain than in the starting decay.
In other words. The power of radiation is greater and greater for some time. For how long?
I have a whimsical challenge for you: come up with problems with numerical solutions that are hard to estimate.
This, like surprisingly many things, originates from a Richard Feynman story:
So what would you ask Richard Feynman to solve? Think of this as the reverse of Fermi Problems.
Number theory may be a rich source of possibilities here; many functions there are wildly fluctuating, require prime factorization and depend upon the exact value of the number rather than it's order of magnitude. For example, I challenge you to compute the largest prime factor of 650238.
(My original example was: "For example, I challenge you to compute the greatest common denominator of 10643 and 15047 without a computer. This problem has the nice advantage of being trivial to make harder to compute - just throw in some extra primes." It has been pointed out that I forgot Euclid's algorithm and have managed to choose about the only number theoretic question that does have an efficient solution.)