Why is euler's number used in the formula for computing for crystalline vacancies?

[Random Student]

From what I know, the formula is Nv=N(e^-Qv/kT)

where:

Nv - total number of vacancies

N - total number of atomic sites

Qv - energy required to

T - temperature

k - Boltzmann's constant = 1.38x10^-23 J/atom-K or 8.62x10^-5 eV/atom-K

Context: So my professor was discussing 0- dimensional defects when I asked the question at the title, but he didn't have the answer and then proceeded to give it to me as a graded homework to provide him an answer. I have no idea where to look for the answer. Hope someone can help me out.

[Sensei]

Did you hear about exponential decay?

https://en.wikipedia.org/wiki/Exponential_decay

Half-life?

https://en.wikipedia.org/wiki/Half-life

Exponential decay equation is slightly modified half-life equation.