Question 1128142: Use the logistic growth model f(x) = 230/1 + 8e^−2x^.
Find f(0). Round to the nearest tenth.
Interpret f(0).
f(0) represents the rate of growth.
f(0) represents the half life.
f(0) represents the carrying capacity.
f(0) represents the initial amount.
f(0) represents the final amount.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
The function as you show it: 230/1 + 8e^−2x^
You seem to have a misunderstanding of the use of "^" to denote exponentiation. "3 squared" is "3^2" -- not "3^2^"
And in a logistic function, everything after the "/" is in the denominator; you need to enclose it in parentheses: 230/(1+8e^(-2x)).
The parentheses around the "-2x" exponent are not required; but they help make the expression more clear.
Now to address your questions....
(1) f(0).
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.
(2) As in a huge number of other applications, f(0) means an initial value.
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.
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.
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