  This paper is concerned with the global boundedness and blowup of solutions
to the Keller-Segel system with density-dependent motility in a two-dimensional
bounded smooth domain with Neumman boundary conditions. We show that if the
motility function decays exponentially, then a critical mass phenomenon similar
to the minimal Keller-Segel model will arise. That is there is a number
$m_*>0$, such that the solution will globally exist with uniform-in-time bound
if the initial cell mass (i.e. $L^1$-norm of the initial value of cell density)
is less than $m_*$, while the solution may blow up if the initial cell mass is
greater than $m_*$.
