This is paper #3 in a series of four papers on "vacuum energy" and inflation. In paper #1 [see EJ1024183] we discussed an example of what we have been calling vacuum energy. It is an energy with negative pressure whose energy density remains constant in an expanding space. We showed that an energy density with these properties exists between the plates of a parallel plate capacitor. In paper #2 [see EJ1024958] we discussed a model universe consisting of vacuum energy with a few galaxies added in as markers, so that we could observe the expansion of space. We discovered that such a galaxy involved a huge release of gravitational potential energy, and we could easily calculate the rate of the Hubble expansion. Throughout, we used standard notation found in introductory physics, so that students could develop an intuition for the new concepts involved in an expanding space. In this, paper #3, we will use the notation of a scale factor "a(t)" to obtain equations similar to those derived from general relativity.