  We apply the Induced Matter Model to a five-dimensional metric. For the case
with null cosmological constant, we obtain a solution able to describe the
radiation-dominated era of the universe. The positive $\Lambda$ case yields a
bounce cosmological model. In the negative five-dimensional cosmological
constant case, the scale factor is obtained as $a(t)\sim\sqrt[]{\sinh t}$,
which is able to describe not only the late-time cosmic acceleration but also
the non-accelerated stages of the cosmic expansion in a continuous form. This
solution together with the extra-dimensional scale factor solution yields the
material content of the model to be remarkably related through an equation of
state analogous to the renowned MIT bag model equation of state for quark
matter $p=(\rho-4B)/3$. In our case, $\rho=\rho_m+B$, with $\rho_m$ being the
energy density of relativistic and non-relativistic matter and $B=\ \Lambda\
/16\pi$ represents the bag energy constant, which plays the role of the dark
energy in the four-dimensional universe, with $\Lambda$ being the cosmological
constant of the AdS$_5$ space-time. Our model satisfactorily fits the
observational data for the low redshift sample of the experimental measurement
of the Hubble parameter, which resulted in $H_0=72.2^{+5.3}_{-5.5}$km s$^{-1}$
Mpc$^{-1}$.
