Under investigation in this paper is an inhomogeneous nonlinear Schrodinger-Maxwell-Bloch system with variable dispersion, nonlinearity and tapered functions which describes the propagation of optical pulses in an inhomogeneous erbium-doped tapered fiber. Under certain coefficient constraints, multi-soliton solutions are obtained by the Darboux transformation method and symbolic computation. In order to study the impact of tapering on soliton dynamics in an inhomogeneous erbium-doped periodic distributed amplification system, a specific form of tapered profile is considered.