Two proofs and a corrected procedure for the generalized exponential function

In a previous article we developed the generalized exponential function as a new growth function. Here we complement that article in three ways: It is proven that any three points of quantities q3 > q2 > q1 at times t3 > t2 > t1 can be connected with a single generalized exponential function. We also prove that any two real quantities of logarithmic relative growth, yi at time ti and yi+1 at time ti+1 , can be connected with the generalized exponential function. Finally, we provide a corrected procedure for the generalized exponential function to convert a sequence of data points yi(ti) into a segmented continuous curve q(t).