When Will the App Store Hit 25 Billion Downloads?
Team Name: _________________________
On February 24th, 2012 my friend Dan noticed this on Apple’s App Store website:
Dan lives in California so the 6:26 PM on his computer is in Pacific Standard Time (PST). He got
really excited about this part:
“Download the 25 billionth app and you could win a $10,000 App Store Gift Card”
He wondered, “When should I start downloading to be the one to win the $10,000?”
1) When Dan checked, 24,658,498,009 apps had been downloaded. If one app were downloaded
every second, how many seconds would it take until the 25,000,000,000th app was downloaded.
2) Convert your answer to #1 into years, days, hours, minutes, and seconds (as in, 1,000,000
minutes = 1 year, 329 days, 10 hours, and 40 minutes).
3) Dan thought it was probably unrealistic that only one app would be downloaded every second.
He wondered what would happen if 1,000 apps were downloaded every second. How long would it
take until the 25,000,000,000th app was downloaded?
4) Dan wondered is 1,000 apps per second was too big of an estimate. He wondered, “what if
10,000 apps are downloaded every minute? Figure out how long it would take until the
25,000,000,000th app was downloaded. Give your answer in years, days, and minutes.
Dan wondered if keeping track of the app store downloads for a while would help him make a better
prediction. He looked at the counter every minute for seventeen minutes, and made this table:
Time
6:26 pm
6:27 pm
6:28 pm
6:29 pm
6:30 pm
6:31 pm
6:32 pm
6:33 pm
6:34 pm
6:35 pm
6:36 pm
6:37 pm
6:38 pm
6:39 pm
6:40 pm
6:41 pm
6:42 pm
6:43 pm
Number of Downloads
24,658,498,009
24,658,507,655
24,658,541,892
24,658,576,918
24,658,610,221
24,658,644,386
24,658,678,549
24,658,712,739
24,658,746,907
24,658,781,962
24,658,815,101
24,658,849,365
24,658,883,552
24,658,917,768
24,658,951,908
24,658,986,195
24,659,020,287
24,659,054,476
5) How many apps were purchased during the 17 minutes?
6) Were more or fewer than one app per second downloaded?
7) What was the average number of apps per second downloaded?
8) What was the average number of apps per minute downloaded?
9) On the next page, plot the time and number of downloads on the graph provided.
YA
>X
Math-Aids.Com
10) Use the points to sketch what you think will keep happening as the app counts up. Draw a line
or a curve to show when you predict it will hit 25 billion apps downloaded. When do you predict it
will happen.
Dan thinks that the trend is basically linear – that the points basically follow a straight line and that
straight line can be used to predict when the 25 billionth app will be purchased. A calculator can be
used to find the straight line that best fits the data.
11) The calculator won’t know how to think about 6:26 PM as a value. Convert the times in this table
to “Minutes after 6:26 PM on 2/24/12”
Time
6:26 pm
6:27 pm
6:28 pm
6:29 pm
6:30 pm
6:31 pm
6:32 pm
6:33 pm
6:34 pm
6:35 pm
6:36 pm
6:37 pm
6:38 pm
6:39 pm
6:40 pm
6:41 pm
6:42 pm
6:43 pm
Minutes after 6:26 PM on
2/24/12
Number of Downloads
24,658,498,009
24,658,507,655
24,658,541,892
24,658,576,918
24,658,610,221
24,658,644,386
24,658,678,549
24,658,712,739
24,658,746,907
24,658,781,962
24,658,815,101
24,658,849,365
24,658,883,552
24,658,917,768
24,658,951,908
24,658,986,195
24,659,020,287
24,659,054,476
Here are instructions for using your calculator to find that line:
(Note: if you need help on the calculator part, raise your hand and a volunteer will come to your
table)
From the home screen, press STAT , 5 , and then ENTER . This sets up the calculator’s built-in list
editor.
Next, press STAT , and ENTER to select the list editor. We’re going to be using L1 and L2 for this
tutorial–if either has data in it, clear the list by selecting the name with the arrow buttons and
pressing CLEAR , then ENTER .
Now enter the X data into L1 and Y data into L2 by using the arrow buttons to select a cell, then
pressing ENTER , typing in the corresponding number, and pressing ENTER again to confirm. The
lists should automatically scale as you add more data.
When done, press STAT , CALC , 4 to select LinReg(ax+b).
Press [VARS], scroll right to highlight Y-VARS, then press [1] [1] to input Y1.
Press ENTER to confirm. The calculator will display your regression equation.
This display means the regression equation for the example in these instructions is Y = 10.5X+.1.
Source: http://www.calcblog.com/performing-a-linear-regression-on-the-ti-83-or-ti-84/
12) Enter the data from Dan’s experiment into your calculator, using the “Minutes after…” and
“Number of Downloads” columns. Then use the LinReg command to find the values for a and b here:
Y = ________ x + ______________
a
b
13) How similar is the calculator’s line to the line you drew? You can compare the slope and yintercept, or press the “Table” button on your calculator to look at a table of values for the calculator’s
rule. How do the table values compare to the actual data?
14) What time would it be 47 minutes after 6:26 PM on 2/24/12?
15) What time would it be 250 minutes after 6:26 PM on 2/24/12?
16) How many minutes after 6:26 PM on 2/24/12 is 6:26 PM on 2/28/12?
17) Use your graph, table, or equation to find how many apps your rule predicts will have been
downloaded 47 minutes after 6:26 PM on 2/24/12.
18) Use your graph, table, or equation to find how many apps your rule predicts will have been
downloaded 48 minutes after 6:26 PM on 2/24/12.
19) Use your graph, table, or equation to find how many apps your rule predicts will have been
downloaded 250 minutes after 6:26 PM on 2/24/12.
20) According to your graph, table, or rule, how many apps are downloaded each minute?
21) Use your graph, table, or equation to find how many apps your rule predicts will have been
downloaded at 6:26 PM on 2/28/12.
22) Use your graph, table, or equation to find how many apps your rule predicts were downloaded at
6:25 PM on 2/24/12?
23) Use your graph, table, or equation to find out how many minutes after 6:26 PM 2/24/12 the
24,660,000,000th app would have been downloaded.
24) Use your graph, table, or equation to find out how many minutes after 6:26 PM 2/24/12 the 25
billionth app would have been downloaded.
25) Knowing that February, 2012 was a leap year (there was a February 29th), on what day does your
rule predict that the 25 billionth app downloaded?
26) At what time on that day does your rule predict that the 25 billionth app was downloaded?
My friend Dan emailed Apple and asked when the actual 25 billionth app was downloaded:
27) How many minutes away from the actual time is your answer?
28) How many minutes did it actually take to get from 24,658,498,009 apps to 25 billion apps?
29) Calculate the amount you were off by as a percentage of the total number of minutes it actually
took.
30) According to your rule, when was the first Apple App Store download?