Monday, February 2, 2015

25 Billion Apps

To find out the exact date of when it would be best to bombard the App Store, and to see when the app store first sold it’s app, I made an equation. I actually tried two ways. For my first way, I tried making a slope by the equation y2-y1,/x2-x2. The y represented the number of apps sold, or downloaded, while the x represented the number of minutes, and the origin would be 6:00pm. Due to that, I decided to use the minutes of 28, and 27, and the numbers 24,658,541,892 and 24,658,507,655. By using those, the slope was 34,347. With that, the equation was: y =34,347x + b. Due to that, I plugged in 24,658,507,655 into y, and 27 for x. After doing that, I got 24,657,583,256 for b. After all this, I concluded that the complete equation would be: y = 34,237x + 24,657,256.
However, even when making this equation, I knew that it wouldn’t be exactly precise since the numbers didn’t go up in the same pattern every minute. Because of that, I decided to make the equation that would be a little bit more “safer” to use. Safer, meaning that it would be a little bit more accurate. To do this, it did take a longer time since I had to find the average of all the amounts of the apps downloaded. Since I knew it was going to take a very long time, I used the excel program. To find out the average, and subtracted the numbers of the apps from 28mins to 27mins, 29mins to 28 mins, and so on. After doing that, I divided them into 16 since there were total of 16. Due to that, the 34,176. By doing the same thing I did above to find the final equation, I got: y = 34176x + 24,657,584,903.
After figuring out this equation, the rest was pretty easy since I just had to plug in the numbers and solve it. To see when it was the best time to download the app, I just plugged in 25,000,000,000 in y and tried to find out what x was.
Moving on, according to my model, the app was first sold in October 11th, 11:12pm, 2010, in Brazilian time. To find this answer, I basically used the equation I made, mentioned above, and plugged 1 in the y which showed the 1st app, and found out the x which was -721488.322 (minutes). With that number, I divided that by 1440, which represents the minutes in 1 day and got the answer of -501.033557134 (days). With those decimals, I multiplied that by 24 to change to hours and again, with the number I got, I multiplied that by 60 to turn that into minutes which was 48 minutes.

Screen Shot 2015-01-31 at 2.09.06 PM.png
(Left- minutes, Middle- apps downloaded, Right - differences between the two numbers)

Basic Explanation of 1st Equation:
6:27pm →  24,658,507,655
6:28pm → 24,658,541,892

Slope equation: y2 - y1/ x2 - x1
24,658,541,892 - 24,658,507,655 / 28 - 27 = 34,237

y = 34,237x +b
(Plug in 27 to x, and 24,658,507,655 to y)

b = 24,657,583,256

y = 34,237x + 24,657,583,256 (Complete equation)

Basic Explanation of 2nd Equation:
6:27pm → 24,658,507,655

Average from 27 mins to 43 mins = 34,176 (Added all the subtracted numbers, then divided it by 16)

y = 34,176x + b
(Substitute 27 to x, and 24,658,507,655 to y)

b = 24,657,584,903

y = 34176x + 24,657,584,903 (Complete equation)

Find out when to download the app:
y = 34,176x + 24,657,584,903
(Plug in 25,000,000,000)

25,000,000,000 = 34,176x + 24,657,584,903
x = 10019.16833 mins

10019.16833 / 1440 (minutes in 1 day) = 6.957755784 (days)

February 24th + 6 (days) = March 1st, 6pm

0.957755788 * 24 = 22.98613891 (hours)
0.98613891 (hours) * 60 = 59 (minutes)
22 hours + 59 minutes = Almost 23 hours
6pm + 23 = 5pm

March 2nd, 5 pm, 2012 (California Time)
March 2nd, 11pm, 2012 (Brazilian Time)

When it sold it’s 1st app:
y = 34,176x + 24,657,584,903
(Plug in 1 in y, and solve x)

1 = 34,176x + 24,657,584,903
x = -721488.322 (minutes)

-721488.322 / 1440 (mins in 1 day) = -501.033557134 (days)
0.033557134 * 24 (change to hour) = 0.80537
0.80537 * 60 = 48 (mins)

February 24, 2012 - 501 days and 48 mins = 2010, October 11th, 5:12 pm (California Time)
October 11th, 2010, 11:12pm (Brazilian Time)


Screen Shot 2015-02-01 at 10.22.37 AM.png

Why the answer is different from actual:
Finding out when was the best time to bombard the app store, I was about 2-3 days off, since according to the internet, it said that it reached 25,000,000,000 on March 5th. I believe the reason for this is because as time goes on, the speed will eventually slow down, and also, this graph in reality would be unpredictable since it isn’t a computer doing by a certain speed, nor does it have a fixed pattern. This is the reason why the graph couldn’t be a parabola nor a straight line. This calculation was used as if it was a “machine” trying to figure it out using the same pattern, and with the exact same speed. However, to calculate to the nearest, this was the way to solve it. Because of this reason, I made an equation using the average to be a little more certain.

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