Chapter 1.3, Problem 59E

Solution

To classify: The logistic function as true or false.

The, the given statement is true.

Given data: The given statement is: The logistic function has two horizontal asymptotes.

Explanation:

A function f of the form $f\left(t\right)=\frac{f_0}{1+e^{-\lambda \left(t-t_0\right)}}$ is known as the logistic function. Here, $f_0$ is the initial (maximum) value of the function, $\lambda$ the parameter that affect the growth rate of the function with time t .

An asymptote of a function is a tangent line) on its graph whose point of contact lies at infinity.

The graph of a logistic function is always of the form shown here in Fig. (1).

  

By the definition of the asymptote there are two horizontal asymptote of a logistic function.

Hence, the given statement is true.