  In this work, we analyse the late-time evolution of the universe for a
particular $f(R)$ gravity model built from an exponential function of the
scalar curvature. Following the literature, we write the field equations in
terms of a suited statefinder function ($y_H(z)$) and considering well
motivated physical initial conditions, the resulting equations are solved
numerically. Also, the cosmological parameters $w_{\rm{DE}}$, $w_{\rm{eff}}$,
$\Omega_{\rm{DE}}$ and $H(z)$ and the statefinder quantities $q$, $j$, $s$ and
$Om(z)$ are explicitly expressed in terms of $y_H(z)$ and its derivatives.
Furthermore, setting an appropriate set of values for the model parameters, the
cosmological parameters as well as the statefinder quantities are plotted, and
their present values (at $z=0$), are shown to be compatible with Planck 2018
observations and the $\Lambda$CDM-model values. Considering updated
measurements from the dynamics of the expansion of the universe, $H(z)$, we
perform an statistical analysis to constrain the free parameters of the model,
finding a particular set of values that fit the data well and predict
acceptable values for the cosmological and statefinder parameters at present
time. Therefore, the $f(R)$ gravity model is found to be consistent with the
considered observational data, and a viable alternative to explain the
late-time acceleration of the universe.
