Analytical time-dependent functions describing the change of the concentration of the solvent S(t) and the homeopathic active substance A(t) during the decimal and centesimal dilution are derived. The function S(t) is a special case of the West-Brown-Enquist curve describing the ontogenic growth, hence the increase in concentration of the solvent during potentization resembles the growth of biological systems. It is proven that the macroscopic S(t) function is the ground state solution of the microscopic non-local Horodecki-Feinberg equation for the time-dependent Hulthen potential at the critical screening. In consequence the potentization belongs to the class of quasi-quantum phenomena playing an important role both in the biological systems and homeopathy. A comparison of the model proposed with recently performed experiment on delayed luminescence of the homeopathic remedy will be also made.