Log relationship between thickness of material and sound absorbed?

[Marcogoodie]

TL;DR

I did an experiement, and found a logarithmic relationship between sound energy absorbed and the amount of mateiral it propagates through. Why is there a logarithmic relationship between the thickness of material and sound absorbed by it?

So I have done an experiment on the amount of sound energy absorbed based on thickness of pvc foam, and found a logarithmic relationship between the two. I've used the frequency-dependent acoustic attenuation power law, which is derived from stokes' law.

Frequency-dependent acoustic attenuation power law:
https://en.wikipedia.org/wiki/Acoustic_attenuation#Power-law frequency-dependent_acoustic_attenuation

My hypothesis is that as sound waves propagate through material, initially, it can bump into more particles and sound waves can be converted into other forms of energy easily, but as the amount of waves decrease when it propagates through thicker material, the chances of it being converted into other forms of energy decrease. Is that correct?

Thanks in advance!

 

[Baluncore]

The energy loss, per unit length, is proportional to the energy propagating.
So the energy is reducing exponentially as it propagates.
What is the inverse of exponentiation?