We explore within the context of brane cosmology whether it is possible to
obtain both early inflation and accelerated expansion during the present ep
och through the dynamics of the same scalar field in an exponential potenti
al. Considerations from successful inflation and viable radiation and matte
r dominated eras impose constraints on the parameters of the potential. We
find that the additional requirement of late time quintessence behavior in
conformity with present observations necessitates the inclusion of two expo
nential terms in the potential.