College Algebra & Trigonometry, 2018a

3.1. EXPONENTIAL AND LOGISTIC APPLICATIONS 147
The graph for a sample logistic relationship is shown below:
1
0.8
0.6
0.4
0.2
y =
1
1+e −0.1t
−40 −20 20 40
The “lazy-s” shape is characteristic of the logistic function. In the early stages,
the relationship shows growth very similar to the simple exponential function,
but, as the function grows larger, the growth decreases and the function values
stabilize. The maximum y value of N is always the horizontal asymptote for the
logistic function.
Negative Exponential Relationships
The Logistic function is very useful for modeling phenomena from the natural
world. Although the simple exponential function is somewhat limited in modeling
natural phenomena, the negative exponential is quite useful. Looking back to
the graph of y =2 x :
20
15
y =2 x
10
5
−4 −2 2 4
−5