  The origin of extended emissions following prompt emissions of short
gamma-ray bursts (SGRBs) is in mystery. The long-term activity of the extended
emission is responsible for promising electromagnetic counterparts to
gravitational waves and, so that it may be a key to uncovering the progenitor
of SGRBs. We investigate the early X-ray light curves of 26 SGRBs with known
redshifts observed with the X-Ray Telescope aboard the {\it Neil Gehrels Swift
Observatory} ({\it Swift}). We find that the exponential temporal decay model
is able to describe the extended emissions comprehensively with a rest-frame
e-folding time of 20 -- 200 seconds. We also estimate the isotropic equivalent
energies of the extended emission with the exponential decay model and of the
prompt emission, compared with those of the prompt emission. Then, it is
revealed that the extended emission is 0 -- 3 orders of magnitude less powerful
than the prompt emission. We find a strong correlation between the expected
maximum luminosity and e-folding time which can be described by a power-law
with an index of $-3.3$ and whose chance probability of $8.2\times10^{-6}$ if
there is no observation bias of {\it Swift}. The exponential temporal decay may
be interpreted to come from the spin-down time scale of the rotation energy of
a highly magnetized neutron star, and/or fallback accretion onto a disk
surrounding a black hole with an exponentially decaying magnetic flux by
magnetic reconnection.
