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

1 Answer
Dec 25, 2016

Answer:

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.