  The basic motivation of this work is to attempt to explain the rapid
primordial inflation and the observed slow late-time inflation by using the
Brans-Dicke theory of gravity. We show that the ratio of these two inflation
parameters is proportional to the square root of the Brans-Dicke parameter $%
\omega$ $(\omega\gg1) $. We also calculate the Hubble parameter $% H$ and the
time variation of the time dependent Newtonian gravitational constant $G$ for
both regimes. The variation of the Hubble parameter predicted by Brans-Dicke
cosmology is shown to be consistent with recent measurements: The value of $H$
in the late-time future is predicted as 0.86 times the present value of $H$.
