Question

How do I graph the logistic function `P(t)=11.5/(1+12.8e^(-0.0266t))` on a TI-83?

Answer 1

See the Socratic graph and the explanation.
graph{x-1/.266ln((12.8y)/(11.5-y))=0 [-10, 10, -5 5]}

Explanation:

graph{x-1/.266ln((12.8y)/(11.5-y))=0 [-100, 100, -20, 20]}
P>0.

The inverse t-sxplicit formula

`t=1/0.266ln((12.8P)/(11.5-P))` is used

The P-intercept ( t = 0 ) is 11.5/13.8=0.8333, nearly.

As `t to -oo, P to 0`.

As `t to oo, P to 11.5`.

So, P = 11.5 is aother horizontal asymptote, besides P = 0.

The second graph is on a befitting scale to reveal this important

characteristic if this logistic function.

I hope that these data and graph will be useful.