Calculating Evolt's "Doomsday"

This is just a fun calculation of when evolt will have no more submitted articles, based on some statistics developed by Isaac Forman.

These calculations are based on the results (as of Jan 2002) of a live graph developed by Isaac Forman.

First, we consider the per-year totals:

yeararticles submitted
1999398
2000254
2001169
2002(incomplete)

Note that we can't include the total for 2002 because the year is incomplete. We could estimate the total for 2002 based on the total for the current number of months, but we have enough data so far that we don't really need to add guessing into the mix.

Now, we need to calculate the decay rate. This will simply be a percentage less than 100% indicating the ratio between the number of submitted articles of one year and its previous year.

yeardecay ratio
1999(undefined)
200063%
200166%

Note that these values are rounded to the nearest percent.

Our mean decay is 64.5%. However, since we rounded our original decay percentages to the nearest percent, it would be incorrect to imply that we have a level of percision to the tenths place. Therefore, we must also round the mean decay percentage to the nearest percentage point: 65%.

Now, we need to create a formula to model the number of submitted articles for a given year. We will call this model A(t), where A is the number of articles in year t and t is the number of years since 1999.

The general decay formula is:

A(t) = P(r/d)^(t*d)

		
	where P is the original amount
	where r is the rate of decay
	where d is the number of divisions of time
	where t is the number of whole time units
		

Here, our P is 398. Our rate of decay (r) is 65% (.65). Our division of time is the same as our whole time unit: 1 year (if our division of time was a month, then d would be 12).

Therefore:

for t>=0|A(t)=398(.65)^t

Now we have a model for the number of articles in year t. But, we're trying to find when the submissions will cease. So, we must set the model equal to 0 and solve for t.

0=398(.65)^t

Here, we realize that there is no solution for t. As t increases, the right side of the equation will become inifinitely closer to 0 but will never reach 0. However, we can still calculate a useful value of t by finding a year when the number of submitted articles will be less than 1.

1 > 398(.65)^t|(1/398) > (.65)^t|log(1/398) > t*log(.65)|-2.6/-.19 < t|13.68 < t

At 14 years, the rate of submission of articles will be less than 1. We can consider this Evolt's "Doomsday."

Find a mistake? Have a better method? Email me.