In the context of viral marketing, does anyone know how they came up with this formula?

Custs(t) = Custs(0) * (K ^ (t/ct +1) - 1) / (K-1)

where Custs(t) -> Number of customers at time t, K -> viral coefficient, and ct -> cycle time

EDIT : Okay I get it.

Basically the number of cycles that have occured at time t equals (t/ct+1)