  Inspired by an exponential $f(R)$ gravity model studied in the literature, in
this work we introduce a new and viable $f(Q)$ gravity model, which can be
represented as a perturbation of $\Lambda$CDM. Typically, within the realm of
$f(Q)$ gravity, the customary approach to investigate cosmological evolution
involves employing a parametrization of the Hubble expansion rate in terms of
the redshift, $H(z)$, among other strategies. In this work we have implemented
a different strategy, deriving an analytical approximation for $H(z)$, from
which we deduce approximated analytical expressions for the parameters
$w_{\rm{DE}}$, $w_{\rm{eff}}$, and $\Omega_{\rm{DE}}$, as well as the
deceleration parameter $q$. In order to verify the viability of this
approximate analytical solution, we examined the behavior of the these
parameters in the late-time regime\textbf, in terms of the free parameter of
the model, $b$. We find that for $b>0$, $w_{\rm{DE}}$ shows a quintessence-like
behavior, while for $b<0$, it shows a phantom-like behavior. However,
regardless of the sign of $b$, $w_{\rm{eff}}$ exhibits a quintessence-like
behavior. Furthermore, it has been deduced that as the magnitude of the
parameter $b$ increases, the present model deviates progressively from
$\Lambda$CDM. We have also performed a Markov Chain Monte Carlo statistical
analysis to test the model predictions with the Hubble parameter, the Pantheon
supernova (SN) observational data, and the combination of those samples,
obtaining constraints on the parameters of the model and the current values of
the Hubble parameter and the matter density. Our findings indicate that this
$f(Q)$ gravity model is indeed a viable candidate for describing the late-time
evolution of the Universe at the background level.
