  In this work, we use power-law cosmology to investigate the evolution of
black holes within the context of metric $f(R)$ gravity satisfying the
conditions provided by Starobinsky model. In our study, it is observed that
presently accelerated expansion of the universe can be suitably explained by
this integrated model without the need for dark energy. We also found that mass
of a black hole decreases by absorbing surroundings energy-matter due to
modification of gravity and more the accretion rate more is mass loss.
Particularly the black holes, whose formation masses are nearly $10^{20}$ gm
and above, are evaporated at a particular time irrespective of their formation
mass. Again our analysis reveals that the maximum mass of a black hole
supported by metric $f(R)$ gravity is $10^{12} M_{\odot}$, where $M_{\odot}$
represents the solar mass.
