  A simple model of quintessential inflation with the modified exponential
potential exp(-\alpha \phi) [A + (\phi-\phi_0)^2] is analyzed in the braneworld
context. Considering reheating via instant preheating, it is shown that the
evolution of the scalar field \phi from inflation to the present epoch is
consistent with the observational constraints in a wide region of the parameter
space. The model exhibits transient acceleration at late times for 0.96 < A
\alpha^2 < 1.26 and 271 < \phi_0 \alpha < 273, while permanent acceleration is
obtained for 2.3 10^{-8} < A \alpha^2 < 0.98 and 255 < \phi_0 \alpha < 273. The
steep parameter \alpha is constrained to be in the range 5.3 < \alpha < 10.8.
