Question 1128142
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The function as you show it: 230/1 + 8e^&#8722;2x^<br>
You seem to have a misunderstanding of the use of "^" to denote exponentiation.  "3 squared" is "3^2" -- not "3^2^"<br>
And in a logistic function, everything after the "/" is in the denominator; you need to enclose it in parentheses:  230/(1+8e^(-2x)).<br>
The parentheses around the "-2x" exponent are not required; but they help make the expression more clear.<br>
Now to address your questions....<br>
(1) f(0).<br>
When x=0, the exponential in the denominator is 1; the whole denominator is then 1+8 = 9.  So f(0) = 230/9 = 25.6 to the nearest tenth.<br>
(2) As in a huge number of other applications, f(0) means an initial value.<br>
It's not part of your question, but another important number in a logistic function is the carrying capacity, which is the limit of the function value as x gets very large.<br>
As x gets very large, the exponential in the denominator goes to 0, and the whole denominator goes to 1+0=1.  So the carrying capacity is the numerator of the logistic function.