Thursday, January 29, 2015

The 25 billion App Challenge

equation - y=34165.8x+2.4658508e10
25th billion app on the 2nd of March 2012 at 4:30PM (6d, 22h, 3min)
Bombard site from 3:30PM - 4:30PM 

Figure 1

How I came up with this model

At first, I put the number of apps downloaded each minute, rate, sum of the rate (respectively, see figure 1). However I later realised that apart from the first column, it was useless as it was easier to do it on the calculator. I searched how to find the equation of the line on a graphing calculator and found a website that brought me through every step. It was very simple but it took a long time since you need to input every set of points into the calculator.  I made the y-axis the apps downloaded and the x-axis the minutes. After that, the calculator gave me the equation of the line (above). 

Now, to find how minutes it would take at this rate until the 25th billion download, I substituted 25 billion into the y and solved the equation. My answer was 9995.14 minutes. Now I made that into days 6 and into hours by using the last two decimals of my previous answer until I had my answer in days, hours and minutes. Then I just added it to February 24 at 6:27PM and got my answer. To convert the different time units, I used an app which made it way easier to calculate.

1. What assumptions have you made in your model
I assumed that the rate of downloads would be steady during the entire time. This is the only way that you can find an accurate slope of the line and therefore y-intercept for the equation. However, this is obviously not the reality. During the night in Europe and the americas, there would less downloads because people are sleeping. Also, people might start bombarding the site as soon as they see that 25 billion is approaching. This would be a dramatic increase in downloads which would make my results incorrect so I made the bombarding time a bit earlier.

2.  Interpret the parameters in your linear model.  What do the units of slope represent?  What does the y-intercept represent?
The units of slope in my graph represent the average increase rate of the downloads. As for my y and x intercept, as I mentioned above, the y-axis is the apps downloaded and the x-axis represents time in minutes. 

3.  According to your linear model, when did the app store sell its first app?  Calculate the answer mathematically then find the actual answer.  If those answers are different, what could explain the difference?
To find the answer to this, all I had to do was to substitute a 1 as y. I solved the equation and got -721730.7366 minutes. The negative means that you need to subtract it from the data collection date. I went through the same process to make the minutes into years, weeks, days, hours and minutes to end up with: 1 year, 19 weeks, 2 days, 2 hours and 9 minutes. Since the subtraction
Figure 2
 was very hard to complete, I subtracted the time from the data collection date using a website (see figure 2) 

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