In this paper, we propose a non-autonomous mathematical model of a single species that is exposed to an environment subject to a pollution tax when the emission of the toxicant exceeds a limit up to which there is no harm to the population. We assume that all emissions exceed the allowable limit and consider the negative effect of tax avoidance. Furthermore, we assume that a born organism carries with it an amount of internal toxicant, and that the amount of toxicant stored in living organisms that die drifts into the environment. We obtain sufficient parametric conditions to guarantee the persistence of the population and also note that the tax coefficient is the key parameter that must be chosen very carefully to maintain the equilibrium level of the population. Finally, for the initial validity of our results we perform some numerical simulations.