  We present several applications of the layered electron gas model to electron
energy loss spectroscopy of free-standing films consisting of $N$ graphene
layers in a scanning transmission electron microscope. Using a two-fluid model
for the single-layer polarizability, we discuss the evolution of high-energy
plasmon spectra with $N$, and find good agreement with the recent experimental
data for both multi-layer graphene with $N<10$, and thick slabs of graphite.
Such applications of these analytical models help shed light on several
features observed in the plasmon spectra of those structures, including the
role of plasmon dispersion, dynamic interference in excitations of various
plasmon eigenmodes, as well as the relevance of the bulk plasmon bands, rather
than surface plasmons, in classifying the plasmon peaks.
