Question

Let f(x)= 24

Answer 1

Answer:

The point of maximum growth is at x = 0.82

Step-by-step explanation:

The given logistic function is :

$f(x)=\frac{24}{1+3\cdot e^{-1.3x}}$

By the graph which is attached below, we can see the maximum value of the logistic function is 24, and the point of maximum growth is at

$\bf y = \frac{24}{2}\\\\\text{So, we can set y = }\frac{24}{2}\text{ and solve for x.}$

The numerators are equal, so the denominators must be equal.

$2=1+3\cdot e^{-1.3x}\\1=3\cdot e^{-1.3x}\\\frac{1}{3}=e^{-1.3x}$

⇒ log 3 = -1.3·x

⇒ -0.4771 = -1.3·x

⇒ x = 0.4771/1.3

⇒ x = 0.82

Hence, The point of maximum growth is at x = 0.82

You can see the logistic curve and the point of maximum growth in the image below.