Graphs of logistic functions (Figures 2 and 4) look suspiciously similar to the graph of the hyperbolic tangent function (Figure 3 in Section 3.9). Explain the similarity by showing that the logistic function given by Equation 4 can be written as where c = (In A)/ k.

Thus, the logistic function is really just a shifted hyperbolic tangent.

Transcribed Image Text:

P() = K[1 + tanh(K(1 – c)] tanh(k(t – c)