Question

a logistic growth model for world population, ( f(x) ), in billions, ( x ) years after 1983 is ( f(x)=\frac{12.57}{1 + 4.11e^{-0.028x}} ). according to this model, what is the limiting size of the population that earth will eventually sustain?
the limiting size of the population that earth will eventually sustain is ( square ) billion.
(type an integer or a decimal.)

Explanation:

Step1: Analyze the logistic function

The general form of a logistic function is \( f(x)=\frac{c}{1 + ae^{-bx}}\), where \(c\) is the limiting value.
In the given function \(f(x)=\frac{12.57}{1 + 4.11e^{-0.028x}}\), comparing with the general form, we can identify the value of \(c\).

Answer:

\(12.57\)