Compiled from various sources, the number of free hours available on an AOL CD over the 90s:
1995: 5 hours
1996: 10 hours
1997: 30 hours
1998: 80 hours
1999: 200 hours
2000: 400 hours
2001: 540 hours
2002: 1000 hours (thanks, pylon)

This can be roughly modeled by

H(t) = 4.8*2.2^t

Where H(t) is the number of hours on an AOL CD at year t (with 1995 = t0).

Now! The average human lifespan is 76 years. Let's assume it won't change too much.

The population of the U.S. grows at a rate of roughly 0.89 percent. Thus, the population can be expressed as

`P(t) = Pop95 * e^(.0089t)`

Where Pop95 is the population of the U.S. in 1995, approximated at 262,800,000.

Thus, `P(t) = 262,800,000 * e^(.0089t).`

If the average lifespan is 76 years (give or take), the average life contains 76*365*24 = 665,760 hours. The average person is 38 years old, so we can divide it by two; the average number of hours anyone has left to live is 332,880.

So, the total number of hours which the U.S.'s population has left to live at time t is:

`M(t) = 332,880 * 262,800,000 * e^(.0089t) = 87,459,840,000,000 * e^(.0089t)`

Now, let's assume that there are roughly 60 AOL CDs behind the counter of every movie theater in America. This is a rather conservative estimate. America has just under 8,000 movie theaters. Thus, the number of free hours in America at time t is:

`HF(t) = 8,000 * 60 * H(t) = 2304000*2.2^t`

Some simple calculations later...

On May 21, 2017, at 6:59 AM, there will be as many free AOL hours in America as there are hours left to live in America. The average AOL CD will contain about 222,378,110 free hours (although the corporation will round it to an even 222 million free hours), and America's population will have reached 320.7 million. Assuming AOL/Time-Warner hasn't gone bankrupt already, they will at this instant, as long as everyone on Earth signs up at the same time.

The moral? Give this writeup to your friends, and join the mass action against the tyrant!

As of March, 2003, AOL prints the following offer on their CD packaging:

1045 HOURS FREE!
for 45 days

Following a few quick calculations, I have surmised that this means one may spend 43 days, 13 hours straight online for free. Alternately, one could spend 23 hours, 13 minutes, and 20 seconds online each day for 45 days, thereby spending equal amounts of time online each day. If AOL offered only 35 more free hours, one could spend the whole month and a half online.

So why does AOL market this way? I have a few ideas. The first is history. AOL's always used free hours as a marketing strategy (mainly because they used to only bill by the hour), and free months just doesn't have the same ring to it. Or maybe AOL Time Warner's marketing department simply thinks that people will be more interested in 1045 free hours that must be used in 45 days than in 45 free, complete, 24-hour days. Or perhaps they think that people who know that they have a quota of hours that they must use up before a certain date will use more of them up, and spend that time becoming addicted to AOL, making themselves better customers. Whatever the reason, there's something faintly absurdist about the legal text that results: 1045 HOUR TRIAL MUST BE USED WITHIN 45 DAYS OF INITIAL SIGN-ON.

Update: I recently picked up an EarthLink CD for the sole reason of acquiring material on which to base an update to this writeup. They have the following sentence printed on the front:

GET 1,000 HOURS FREE.

Nevermind how few style guides would recommend using a comma in a four-digit number; here's the catch:

The 1,000-hours offer must be used within the first 45 days of subscription.

Just for the sake of completeness, here's the result of the math: One may spend 41 days, 16 hours straight on EarthLink for free. Or, one could spend 22 hours, 13 minutes, and 20 seconds online each day for 45 days. And if anyone really picks an internet service provider on the basis of time-limited free hours, that means that you can get one hour a day less sleep going with AOL. Have a fun month-and-a-half!

Another update: In June 2004 I received a copy of the AOL 9.0 Optimized CD in the mail with a FireWire/USB hard drive enclosure, which is strange as I find most potential AOL users are not geeky enough to assemble their own external storage devices. In any case, the CD packaging advertises

1099 HOURS FREE!
for 50 days

Though AOL now offers 54 more free hours than they used to, this is actually fewer hours per day. One may spend 21 hours, 58 minutes, and 48 seconds online each day for 50 days for free or, alternately, stay connected to AOL constantly for 45 days, 19 hours.

1099 HOUR TRIAL MUST BE USED WITHIN 50 DAYS OF INITIAL SIGN-ON. TO AVOID BEING CHARGED A MONTHLY FEE, SIMPLY CANCEL BEFORE TRIAL PERIOD ENDS. Premium services carry surcharges, and communication surcharges may apply in certain areas, including in AK, even during trial time. Members may incur telephone charges on their phone bill, depending on their location and calling plan, even during trial time. Available to new members in the US, age 18 or older; a major billing method is required. We may be optimizing some of your computer settings to enhance your experience on AOL. AOL for Broadband requires a separate high-speed connection. High-speed connections are available in certain areas only.

AOL now simply offers 50 free days of service with "unlimited hours," which is far less entertaining to the mathematically inclined, but probably makes more sense. This change is truly the end of free AOL hours.

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