College Algebra & Trigonometry, 2018a

3.1. EXPONENTIAL AND LOGISTIC APPLICATIONS 145
These values for the area under the curve are actually the same values as those
for the slope of the tangent line in the previous graphs. If you ask the question,
”Where should you draw the second vertical line so that the area under the curve
is equal to exactly 1?” then just like the slope question, the answer is e ≈ 2.71828.
This is how the value of e was determined and why it is used to represent these
exponential relationships.
Logistic Relationships
Let’s consider the graph of y =2 x :
20
15
10
5
−4 −2 2 4
−5
If we extend the x-axis out further past x =4, we would see that the y values for
this relationship will grow very quickly, as they continue doubling.
1,000
800
600
400
200
−4 −2 2 4 6 8 10