Tuesday, February 3, 2015

App Store (Math)

According to my calculations, the best time to bombard the App Store with downloads so that you could win the prize would be March 2nd, around 3:28 Pacific Standard time. However, if you were living in Brazil, the time difference would be around 6 hours. For Brazil, the best time would be around 9:28. How did I get that answer?

Well, I knew that I needed to make a graph, in order to predict the increase of app downloads over time and when the store would hit 25 billion. In other words,  I needed a y = mx+b model. I knew y would have to be the amount of downloads, and x would be minutes that have passed. I would use 25 billion as my y in order to find x. So, I needed to find m, or the slope/rate, and b. First, I tried finding my slope.

I got my rate from looking at the 17 screenshots Mr. Oskness had on his website. The screenshots captured the number of apps downloaded. Each one was taken after a minute passed. I wrote these numbers down into a chart in my notebook here:

My chart wasn't completely accurate. The reason why is that some of the numbers were right in the middle of changing, so it was unclear what the exact number was. You either had to guess what was the previous number, guess what was the next number and to choose one. Because of that, my numbers and what I interpreted from the pictures will be different from another students, making it less accurate. Here's some examples of what the pictures looked like:

Also, the pictures were probably weren't taken at the exact time a minute passed. In those few seconds, the number has gone up hundreds. Therefore, we don't have the exact rate of how the minutes pass.

The next step was to find the rate. Using my graph, I took the difference of the numbers between each minute. I did not have a consistent rate, which makes my graph even less accurate. I took the average of the numbers to find a general rate. Then, to be safe, I inserted the graph into the calculator as a scatter plot and generated a line equation. The rate is probably not very accurate, but it was close enough. I got a rate of 34,160 apps downloaded per minute. This line generation also gave me b, which was 24,658,508,000. The final product was  y = 34,160x - 24,658,000.

I inserted 25 billion into the way and solved the problem by hand. I got the answer 9, 996 minutes. It was difficult to transfer that into days, hours, and minutes. I first divided that number by 60, to get hours. I got 166.61. I assumed that the .61 represented minutes left over. Then I divided that number by 24, to get days. The answer was ultimately 6 days, 9 hours and a minute from the starting point. I assumed the starting point was February 24th, and added the time from there.

The final answer was, again, March 2nd at 3:28 Pacific Standard time. However, this time was not completely accurate due to my assumptions and generalizations. However, I did get the correct day.

Next, I needed to find out when the first app was ever downloaded. I inserted 1 into my line and tried to find the time. I got the answer 1 years and 11 months ago from Febuaray 24, 2012. So that would be roughly March 24, 2010. The actual answer is July 10, 2008. It was only few months of difference but that's probably because my graph was based on minutes and only recent downloads instead of years and billions of downloads. Plus, my graph isn't precise or completely accurate. However, I managed to get near the right answer.

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