The Parker Solar Probe (PSP) achieved its first orbit perihelion on 2018 November 6, reaching a heliocentric distance of about 0.165 au (35.55 R☉). Here, we study the evolution of fully developed turbulence associated with the slow solar wind along the PSP trajectory between 35.55 R☉ and 131.64 R☉ in the outbound direction, comparing observations to a theoretical turbulence transport model. Several turbulent quantities, such as the fluctuating kinetic energy and the corresponding correlation length, the variance of density fluctuations, and the solar wind proton temperature are determined from the PSP Solar Wind Electrons Alphas and Protons (SWEAP) plasma data along its trajectory between 35.55 R☉ and 131.64 R☉. The evolution of the PSP derived turbulent quantities are compared to the numerical solutions of the nearly incompressible magnetohydrodynamic (NI MHD) turbulence transport model recently developed by Zank et al. We find reasonable agreement between the theoretical and observed results. On the basis of these comparisons, we derive other theoretical turbulent quantities, such as the energy in forward and backward propagating modes, the total turbulent energy, the normalized residual energy and cross-helicity, the fluctuating magnetic energy, and the correlation lengths corresponding to forward and backward propagating modes, the residual energy, and the fluctuating magnetic energy.