  We investigate cosmological consequences of a class of exponential $f(R)$
gravity in the Palatini formalism. By using the current largest type Ia
Supernova sample along with determinations of the cosmic expansion at
intermediary and high-$z$ we impose tight constraints on the model parameters.
Differently from other $f(R)$ models, we find solutions of transient
acceleration, in which the large-scale modification of gravity will drive the
Universe to a new decelerated era in the future. We also show that a viable
cosmological history with the usual matter-dominated era followed by an
accelerating phase is predicted for some intervals of model parameters.
