Saturation Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy

For

f(x) = \dfrac{50}{1+e^{-x}}

, state the saturation level and the value at

x=0

. What does the saturation represent physically?

Solution

1
Saturation level (horizontal asymptote): $\lim_{x\to\infty}f(x)=\frac{50}{1+0}=50$ .
2
At $x=0$ : $f(0)=\frac{50}{1+1}=25$ . Physically: $50$ is the maximum capacity the system can reach; growth slows and eventually stops there.

Answer

Saturation at

50

;

f(0)=25

The numerator

L=50

sets the upper bound that the function asymptotically approaches. At

x=0

, the logistic function is always at

L/2

, its inflection point.

About Saturation

Saturation is the phenomenon where a growing quantity approaches a limiting value asymptotically, with the rate of growth decreasing as the limit is approached.

Learn more about Saturation →

More Saturation Examples

Example 1 medium

The logistic function [formula] models population growth. Find [formula], [formula], and [formula].

Example 2 hard

Identify the four parameters [formula], [formula], [formula] in [formula] and describe the qualitati

Example 4 medium

A bacteria culture saturates at [formula] cells. At time [formula] there are [formula] cells. Write

← All Saturation Examples Saturation Concept

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