[en] The possibility of using the model of fast growth (MFG) for describing experimental data on pions charge exchange on protons at small momentum transfers is considered. An assumption is put forth on the logarithmic growth with the Coulomb phase energy in elastic π^+-p scattering. The description of the model is given and the method of taking into account radiative corrections to the ampitude of π^+-p scattering at small angles is described. It is shown that MFG permits to describe well all experimental data available on charge exchange at momenta P lab. > 6 GeV/c including the recent Serpukhov data on polarization at P lab. = 40 GeC/c