  In this paper we present a new cosmological inflationary model which is
constructed using the Ivanov-Salopek-Bond method with a logistic generating
function. We derive the inflationary observables as well as the duration and
temperature of the subsequent reheating epoch of our model exactly, with no
need to recur to the slow roll approximation. The obtained scalar spectral
index and tensor-to-scalar ratio of perturbations fall comfortably within the
range of the measurements presented by the Planck collaboration. On the other
hand, for the reheating era, our model predicts a relatively small number of
e-folds and thus high temperatures, still within range of Planck's bounds.
