So it's now almost 30 years after Chernobyl, so if I read this naively: > When this photo was taken, 10 years after the disaster, the Elephant’s Foot was only emitting one-tenth of the radiation it once had. the Elephant's foot will currently have 1/1000th of the original radioactivity it had right after the disaster, and 10 years from now it will be down to 1/10,000th. At that rate it would be indistinguishable from…
You are right, in that your guess is wrong ;-). Total activity decrease in realistic "atomic waste" is not at all exponential. Try a simple example: Take a mixture of two isotopes. The one isotope has a half-life of 1 year and there's so much of it, that the activity is 10 decays/second. There's also a second isotope in the mix, with a half-life of 100 years, but there's 100 times as much of it, so that in total, you…
What yoU end up with is a system of differential equations, which are actually easy to solve if you know how, but that level of calculus is beyond what most folks have studied.
Anyway, a situation that tends to be common is that you have one sort of longer lived isotope which ends up producing another isotope which decays fairly fast along a multi-step chain. This ends up producing a fairly high level of radiation for a significant time in a pseudo steady state. But it depends on the details.