Using Semi-Log Graphs

Graphs on the semi-log paper are more linear, than those on regular graph paper. They also are to a much different scale than graphs on rectangular graph paper because the vertical axis increases by exponential powers. 

The main reason to graph data on semi-log graph paper is that when dealing with logs and exponential functions, the number increase rapidly, and semi-log paper allows you to plot all of your points, instead of only being able to plot 2 or 3 like on rectangular graph paper. Basically, if the graph is increasing exponentially, then using semi-log graph paper is easier. 

One advantage to using semi-log graph paper is that you are able to graph exponentially increasing functions that have large numbers. One disadvantage is that you can't really see the shape of the graph because semi-log graph paper produces a more linear looking line. 

A graph that has a logarithmic scale, and that has been graphed on semi-log graph paper could be misleading because the scale on semi-log graph paper is much different. It condenses the plot so that you can fit all of your points on the paper. 

The Significance of Exponential Functions (Monica Blog)

The main thing I learned from Monica's talk was that information spreads quicker than any of us can imagine. As the negative information spreads, and more and more people see it, life becomes less worth living for the victim. When she was talking about how many people who are victims of cyberbullying commit suicide, that's when her message really hit me, and made me realize how serious this problem is. 

If every hour, 3 new people get the information, then the chart looks like this:
x     y
0     1
1     3
2     9
3     27
4     81
5     243
6     729
7     2187
8     6561
9     19683
10   59049
11   177147 
12    531441
13    1594323
14    4782969
15    14348907

The equation of these data points is y=3^x
When you try to graph these points on the graph paper, you can only do the first three because after that, the number increase my too much and are therefore too large to graph on the paper.

If every hour 10 new people get the information, then the chart looks like this:
x     y
0     1
1     10
2     100
3     1000
4     10000
5     100000
6     1000000
7     10000000
8     100000000
9     1000000000
10   10000000000
11   100000000000
12   1000000000000 
13   10000000000000
14   100000000000000
15   1000000000000000

The equation of these data points is y=10^x
With these points, the numbers increase so rapidly that on the graph, you can only plot the first two points. 

If the information was passed on to 10 people every 15 seconds then after only one minute, 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 would have the information. This number is so large that it is hard for us to grasp that concept of how many people are receiving information per minute if only 10 people receive it every 15 seconds. (y=10^60)

If the information was passed on to 100 people every time someone "clicks", the number after only one minute would be way too large for us to imagine.

Every time you increase the number of people receiving the information, the graph gets steeper. For example the graph of y=10^x is much steeper than the graph of y=3^x. This is because as you increase the base, the numbers you get when you plug in a number for x get drastically bigger. 

In conclusion, it is impossible for us to grasp just how many people are seeing information on the internet per minute, or even second.