We report an analogously programmable memristor based on genuine electronic resistive switching combining ferroelectric switching and electron tunneling. The tunnel current through an 8 unit cell thick epitaxial Pb(Zr[0.2]Ti[0.8])O[3] film sandwiched between La[0.7]Sr[0.3]MnO[3] and cobalt electrodes obeys the Kolmogorov-Avrami-Ishibashi model for bidimensional growth with a characteristic switching time in the order of 10^-7 seconds. The analytical description of switching kinetics allows us to develop a characteristic transfer function that has only one parameter viz. the characteristic switching time and fully predicts the resistive states of this type of memristor.