  We study the linear instability and the nonlinear dynamical evolution of the
Reissner-Nordstr\"om (RN) black hole in the Einstein-Maxwell-scalar theory in
asymptotic flat spacetime. We focus on the coupling function
$f(\phi)=e^{-b\phi^2}$ which allows both the scalar-free RN solution and
scalarized black hole solution. We first present the evolution of system
parameters during dynamic scalarization. For parameter regions where
spontaneous scalarization occurs, we find that the evolution of the scalar
field at the horizon is dominated by the fundamental unstable mode from linear
analysis at early times. At late times, the nonlinear evolution can be viewed
as the perturbation of scalarized black holes.
