Final answer:
To find the initial value of the logistic model f(x)=250/(1+9e^-0.813x), set x to 0 and calculate, resulting in an initial value of 25.
Step-by-step explanation:
The initial value of a logistic model represents the value of the function when x is equal to zero. For the given logistic model f(x) = \frac{250}{1 + 9e^{-0.813x}}, we can find the initial value by substituting x = 0 into the equation. This simplifies the equation since the exponential part becomes e^{0}, which equals 1.
Let's calculate the initial value step by step:
Substitute x = 0 into the function: f(0) = \frac{250}{1 + 9e^{-0.813(0)}}.
Simplify the exponent: e^{0} = 1.
Plug the exponent value into the function: f(0) = \frac{250}{1 + 9(1)}.
Calculate the denominator: 1 + 9 = 10.
Finally, divide 250 by 10: f(0) = \frac{250}{10} = 25.
Therefore, the initial value of the logistic model is 25.