Databases Reference
In-Depth Information
Example 1.6 : Let x = 1/2. Then
1
2
1
8
1
48
1
384
e
1/2
= 1 +
+
+
+
+
or approximately e
1/2
= 1.64844.
Let x =−1. Then
1
2
−
1
6
1
24
−
1
120
1
720
−
1
5040
e
−1
= 1−1 +
+
+
+
or approximately e
−1
= 0.36786.
2
1.3.6
Power Laws
There are many phenomena that relate two variables by a power law, that is, a
linear relationship between the logarithms of the variables. Figure 1.3 suggests
such a relationship. If x is the horizontal axis and y is the vertical axis, then
the relationship is log
10
y = 6−2 log
10
x.
10,000,000
1,000,000
100,000
10,000
1000
100
10
1
1
10
100
1000 10,000
Figure 1.3: A power law with a slope of−2
Example 1.7 : We might examine book sales at Amazon.com, and let x rep-
resent the rank of topics by sales. Then y is the number of sales of the xth
best-selling book over some period. The implication of the graph of Fig. 1.3
would be that the best-selling book sold 1,000,000 copies, the 10th best-selling
book sold 10,000 copies, the 100th best-selling book sold 100 copies, and so on
for all ranks between these numbers and beyond. The implication that above
