The task of mathematical modeling the cancer is a monumental challenge. Past and current mathematical models have been proposed to examine the tumor growth and the discussions and challenges still remain. The present paper concerns with a basic model proposed by Kuznetsov, Makalkin and Taylor for immunogenic tumors. Another standpoint is taken into account, namely, the existence of a state space exact linearization for the dynamics of the model is approached. The basic 2d case is tested for the moment. The important result is that the 2d model admits a state space exact linearization, in feasible conditions for the parameters. The paper continues some recent work on this subject. The control u involved in the method can have a graphical evaluation, based on some parameters values from the literature and experiments. Some useful evaluations of it are done using the Maple Software. The analysis would be useful in further analysis, together with the extension to the 3d model.