  In this paper we investigate a simple parameterization scheme of the
quintessence model given by Wetterich (2004). The crucial parameter of this
model is the bending parameter $b$, which is related to the amount of dark
energy in the early universe. Using the linear perturbation and the spherical
infall approximations, we investigate the evolution of matter density
perturbations in the variable dark energy model, and obtain an analytical
expression for the growth index $f$. We show that increasing $b$ leads to less
growth of the density contrast $\delta$, and also decreases the growth index.
Giving a fitting formula for the growth index at the present time we verify
that the approximation relation $f\simeq\Omega_m^{\alpha}$ also holds in this
model. To compare predictions of the model with observations, we use the
Supernovae type Ia (SNIa) Gold Sample and the parameters of the large scale
structure determined by the 2-degree Field Galaxy Redshift Survey (2dFGRS). The
best fit values for the model parameters by marginalizing on the remained ones,
are $\Omega_m=0.21_{-0.06}^{+0.07}$, $w_0=-2.05_{-2.05}^{+0.65}$ and
$b=4.05^{+7.05}_{-2.25}$ at $1\sigma$ confidence level. As a final test we
calculate the age of universe for different choices of the free parameters in
this model and compare it with the age of old stars and some high redshift
objects. Then we show that the predictions of this variable dark energy model
are consistent with the age observation of old star and can solve the "age
crisis" problem.
