Final answer:
The carrying capacity in the logistic model f(x) = (1000)/(1+500e^-0.402x) is 1000, as this is the value the function approaches as x tends toward infinity indicating the maximum sustainable population size.
Step-by-step explanation:
In the given logistic model f(x) = \(\frac{1000}{1 + 500e^{-0.402x}}\), the carrying capacity can be determined by examining the behavior of the function as x increases without bound. As x approaches infinity, the term 500e^{-0.402x} approaches zero, and the entire denominator approaches 1. Therefore, the function f(x) approaches the value of 1000, which is the carrying capacity of this logistic model.
Carrying capacity (K) is a concept used to describe the maximum population size that a particular environment can sustain indefinitely. In the context of the logistic growth model, when the population size reaches the carrying capacity, growth slows down and the population size stabilizes.