SOLUTION: The graph of a logistic growth function y= (c)/(1+ae^-rx) reaches its point of maximum growth, where y=c/2 . Show that the x coordinate of this point is x= ln a/r . I saw that y

Question 718222: The graph of a logistic growth function y= (c)/(1+ae^-rx) reaches its point of maximum growth, where y=c/2 . Show that the x coordinate of this point is x= ln a/r .
I saw that y equaled to things so I set those equal to each other.
C/(1 + ae^-rx) = C/2
1+ae^-rx = 2
ae^-rx = 1
ln (ae^-rx) = ln (1)
ln (ae^-rx) = 0 ???
I am not sure how to solve this question, can you also explain the process. Thanks!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The graph of a logistic growth function y= (c)/(1+ae^-rx) reaches its point of maximum growth, where y=c/2 . Show that the x coordinate of this point is x= ln a/r .
I saw that y equaled two things so I set those equal to each other.
C/(1 + ae^-rx) = C/2
1+a*e^(-rx) = 2
ae^-rx = 1
e^(-rx) = 1/a
----
-rx = -lna
------
x = (1/r)ln(a)
OR
x = ln[a^(1/r)]
==================
Cheers,
Stan H.
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