Answer:
x = 0.82
Step-by-step explanation:
I am assuming your logistic function is
[tex]f(x) = \frac{24 }{1 +3e^{-1.3x} }[/tex]
The graph of the function is asymmetric, the maximum value is 24, and the point of maximum growth is at
y = 24/2
So, we can set y = 24/2 and solve for x.
[tex]\frac{24 }{ 2} = \frac{24 }{1 +3e^{-1.3x} }[/tex]
The numerators are equal, so the denominators must be equal.
[tex]2 = 1 +3e^{-1.3x}[/tex]
[tex]1 = 3e^{-1.3x}[/tex]
[tex]\frac{1 }{3}=e^{-1.3x}[/tex]
log3 = -1.3x
-0.4771 = -1.3x
x = 0.4771/1.3
x = 0.82
The point of maximum growth is at x = 0.82.
You can see the logistic curve and the point of maximum growth in the image below.
