Mathematical models for pollutant transport in semi-infinite aquifers are based on the advection-dispersion equation (ADE) and its variants. This study employs the ADE incorporating time-dependent dispersion and velocity and space-time dependent source and sink, expressed by one function. The dispersion theory allows mechanical dispersion to be directly proportional to seepage velocity. Initially the aquifer is assumed contaminant free and an additional source term is considered at the inlet boundary. A flux type boundary condition is considered in the semi-infinite part of the domain. Laplace transform technique (LTT) is then applied to obtain a closed form analytical solution. The effect of source/sink term as a function in the one-dimensional advection-dispersion equation is explained through the graphical representation for the set of input data based on similar data available in hydrological literature. Matlab software is used to obtain the graphical representation of the obtained solution. The obtained analytical solution of the proposed model may be helpful in the groundwater hydrology areas.