  In this note we are concerned with the notion of amenable representation type
as defined in a recent paper by G\'abor Elek. Roughly speaking, an algebra is
of amenable type if for all $\varepsilon > 0$, every finite-dimensional module
has a submodule which is a direct sum of modules which are small with respect
to $\varepsilon$ such that the quotient is also small in that respect. We will
show that the tame hereditary path algebras of quivers of extended Dynkin type
over any field $k$ are of amenable type, thus extending a conjecture in the
aforementioned paper to another class of tame algebras. In doing so, we avoid
using already known results for string algebras. We also show that path
algebras of wild acyclic quivers over finite fields are not amenable.
