It's more complicated than that. As you point out, you don't have just one isotope, you have a whole grab bag of stuff. Here's the wrench in the works that adds the complexity, when a radioactive isotope decays it doesn't just go away, it decays into another isotope, sometimes one that is also radioactive and with its own half life.
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.
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.