  Let $\mathbf{A}$ be a finite algebra generating a finitely decidable variety
and having nontrivial strongly solvable radical $\tau$. We provide an improved
bound on the number of variables in which a term can be sensitive to changes
within $\tau$. We utilize a multi-sorted algebraic construction, amalgamating
the methods developed by Valeriote and McKenzie for the investigation of
strongly abelian locally finite decidable varieties with those of Idziak for
locally finite congruence modular finitely decidable varieties.
