Based on the five-dimensional cosmological model with a big bounce, by using the forms of the effective equation of state for dark energy,the expression of the interesting function f(z) is given in this model.Furthermore,the evolution of some cosmological quantities with the redshift z is presented. In addition, it is shown that the evolution of the dimensionless density parameters Ωdm, Ωde and deceleration parameter q for the first case is the best fit one,that consists with the present observations.