Max Faye's Blog Post 4

Instantaneous Rate of Change Lesson
Hey class!

My name is Professor Faye and I will be teaching you about Instantaneous Rate of Change, why it is important, and how to determine it. 

Instantaneous rate of change is an important analytical tool for many different careers. It can help you determine everything from how much profit a store is making at a certain time to how many votes a candidate is receiving at a certain time.

Today we are going to look at Twitter and how it relates at instantaneous rate of change. Below is a chart showing how many Tweets were sent per day each year since Twitter's start in 2006. We will find the approximate instantaneous rate of change in Tweets sent per day in 2010. 

The first step in finding the instantaneous rate of change is to picture these points as a graph, and imagine the slope between these lines. 

The instantaneous rate of change can be found by finding the average of the slopes of the secent lines from around 2010 (so the secent line from 2009 to 2010 and from 2010 to 2011) and averaging those together.

We will begin by finding the slope of the secent line from 2009 to 2010. We do this by dividing the average number of Tweets sent per day in 2010 minus the average number of Tweets sent per day in 2009 by the difference in years from 2010 to 2009.

The equation for this would look like:
(50,000,000-2,500,000)/(2010-2009), or 47,500,000/1.
Therefore, the slope of the secent line from 2009 to 2010 is 47,500,500.

We will apply this same process to find the slope of the secent line from 2010 to 2011. Once again, we would do this by dividing the average number of Tweets sent per day in 2011 minus the average number of Tweets sent per day in 2010 by the difference in years from 2011 to 2010.

This equation would look like:
(200,000,000-50,000,000)/(2011-2010), or 150,000,000/1.
This means that the slope of the secent line from 2011 to 2010 is 150,000,000.

The next step in the process is to find the average of the two slopes to approximate the instantaneous rate of change in 2010. 

The equation to do this would be
(150,000,000+47,500,500)/(2), or 197,500,500/2 which is 98,750,250.

This means that the approximate instantaneous rate of change for 2010 is 98,750,250 Tweets per day. 

This provides an example of just how quickly Twitter is growing, and how important it is to understand the power of social media. It is becoming a huge part of every day life, as evidenced by how many Tweets are sent each day.

Any questions?