Number of conjugacy classes in general affine group of fixed degree over a finite field is polynomial function of field size

Statement
Suppose $$n$$ is a natural number. Then, there exists a polynomial function $$f$$ of degree $$n$$ such that, for any prime power $$q$$, the number of conjugacy classes in the  general affine group $$GA(n,q)$$ (i.e., the general affine group of degree $$n$$ over the finite field of size $$q$$) is $$f(q)$$.

General observations
Below, we list some general observations about the polynomial in $$q$$ giving number of conjugacy classes in $$GA(n,q)$$.