  The asymptotic behaviour is studied of exponentially bounded sequences of
codimensions of identities of algebras with unity. A series of algebras is
constructed for which the base of the exponential increases by exactly one when
an outer unity is adjoined to the original algebra. We show that the
PI-exponents of unital algebras can take any value greater than two, and the
exponents of finite-dimensional unital algebras form a dense subset of the
domain [2,$\infty$).
