  In an absorbing or an active host medium characterized by a complex
refractive index $n_2=n_2'+{\rm i}n_2''$, our previously developed modified
dipole long-wave approximation (MLWA) is shown to essentially overly with the
exact Mie theory results for spherical nanoparticle with radius $a\lesssim 25$
nm ($a\lesssim 20$ nm) in the case of Ag and Au (Al and Mg) nanoparticles. The
agreement for Au and Ag (Al and Mg) nanoparticles, slightly better in the case
of Au than Ag, continues to be acceptable up to $a\sim 50$ nm ($a\sim 40$ nm),
and can be used, at least qualitatively, up to $a\sim 70$~nm ($a\sim 50$ nm)
correspondingly. A first order analytic perturbation theory (PT) in a
normalized extinction coefficient, $\bar\kappa=n_2''/n_2'$, around a
nonabsorbing host is developed within the dipole MLWA and its properties are
investigated. It is shown that, in a suitable parameter range, the PT can
reliably capture the effect of host absorption or gain on the extinction
efficiency of various plasmonic nanoparticles.
