The effective-mass-approximation differential equations appropriate for impurities in a graphite host are constructed and are used to solve self-consistently for the screening response surrounding a single intercalant atom. The screening cloud is found to have a very slow algebraic decay with a characteristic length of 3.8 Å in the case studied. This rather long length is due to both the semimetallic and the two-dimensional character of graphite. A Thomas-Fermi description of screening is found to be adequate, but a linear-response theory is not. From these results we conclude that the transferred charge in alkali-metal-graphite intercalation compounds is distributed nearly homogeneously on a carbon plane. We discuss recent theoretical and experimental work in light of these results.