Exponential decay constant of a set of geometric means applied to arithmetic means??

I have the geometric mean of the population alive after an pandemic over time with the geometric mean taken over various different simulations.

I have found that this fits an exponential decay with decay constant 1.9 extremely well.

I want to apply this trend to different countries but that data I have for that is sparse and is all in arithmetic means.

My question is can I apply the same decay constant taken from geometric means to arithmetic means of the same data?

Many Thanks