What is the difference between intial and existing features in TimeScope?

In TimeScope, initial features refer to the number of features in this layer that you want built before the layer’s TimeScope start date.  Existing features refer to a simple number that is added to initial features to create a basis for the exponential growth.  For example, if a town of 10,000 is going to grow at 5% per year and the TimeScope layer represents only new buildings, then there are 10,000 existing features, 0 initial features, and the growth rate is 5%.  For more information, the equation being used, and some examples, see Specifying a TimeScope build rate.