I know that if I have a sample of a certain radioactive isotope with total mass $x_0$, then I can calculate how much of that mass is left after $t$ hours using $ x = x_0 \cdot e^{- \lambda t} $. I also know that this works the same if instead of mass I use Becquerels or total number of particles.
But what about the equivalent dose? That is, if it takes $t$ hours for the sample's mass to decrease by half, can I expect a measurement in $\mu$Sv from a geiger counter to also halve after $t$ hours (assuming the background radiation in negligible and I take both measurements at the same distance from the sample)? I would expect that measurement to have some sort of half-life, the question is whether or not I can use the same equation $ x = x_0 \cdot e^{- \lambda t} $, with the same constant $\lambda$.
