From: the October 1993 issue of _MIX_ Magazine, Audio Village ad Industry Fact - When Elvis Presley died in 1977 there were 37 Elvis impersonators in the world. - Today there are 48,000. - If the current trend continues, by the year 2010, one out of every three people in the world will be an Elvis impersonator.

Naturally, this intrigued me, there's two points given, so it's trivial to solve for a linear equation.

Using a script I wrote to calculate differences in time and convert it to standard average sidereal years:

# timescript -f 1977-8-16-0-0-0 -t 1993-10-1-0-0-0 16 years, 1 month, 15 days, 11 hours, 1 minute, and 34 seconds. Alternatively, 16.1256589371767 years.

This yields an E (Elvis impersonators per year) of around 2974.32806850604397291147 per year and the subsequent linear regression:

2974.32806850604397291147*t+37 where t is the number of years since Elvis's death. 2010 was 33 years away, so that implies:

(2974.32806850604397291147) * (33) + 37 = 98189.82626069945110607851 Elvis Impersonators. Far short of their calculation. In researching more information, I found the Wikipedia article on Elvis Impersonators which gives this quote:

"There are now at least 85,000 Elvis’s around the world, compared to only 170 in 1977 when Elvis died. At this rate of growth, experts predict that by 2019 Elvis impersonators will make up a third of the world population." - The Naked Scientists, 3rd December, 2000.

Using that information:

# timescript -f 1977-8-16-0-0-0 -t 2000-12-3-0-0-0 23 years, 3 months, 17 days, 12 hours, 55 minutes, and 33 seconds. Alternatively, 23.298018020482 years.

From which we find E equivalent to 3641.08225538427145370131 and the resulting equation:

(3641.08225538427145370131) * (42) + 170 = 153095.45472613940105545502 Elvis Impersonators. Somewhat more respectable, but still a fraction of the 2,000,000,000 expected.

It's worth noting that these articles quote experts. Furthermore, it's known that populations tend to grow as exponential functions of e (the natural number -- 2.71828182846 is a good approximation). Since my equations prove that the projected rate of growth is superlinear, it's reasonable to bow to Biology and expert opinion.

In doing all this, I've come to the logical conclusion that the growth of the population of Elvis Impersonators is in fact a natural function.

Natural functions follow the form e^(t/k) + P0. Given that equation, we find from the later article:

e^(42/k)+170 = 2000000000

e^(42/k) = 1999999830

ln 1999999830 = 42/k

k * ln 1999999830 = 42

k = 42/ln(1999999830)

k = 1.96111272846496985794

The older data gives a k of 1.08785808443098960307, incidentally.

The k portion of the equation usually provides a measure of population loss due to predation, old age, illness, and other environmental pressures with the amount of time until an Elvis Impersonator matures to recruitment age (where they can reproduce) and how frequently the reproduce. In short, the higher the k, the greater the obstacles to continued population growth. k is normally broken down into other functions representing these factors individually. I lack expertise in the area of Elvis Impersonator study, so I'm drawing my conclusions from data provided to me by peer-reviewed experts.

The older k estimates a much lower k than the new data. It's unlikely that recruitment age has changed, so it suggests that times have grown ever tougher for Elvis Impersonators. One can assume this is due to limited income from a relatively constant number of clubs willing to accept an Elvis Impersonator act.

Note as well that older Elvises seem to require increased amounts of food to support their increased girth, thus as the population of Elvis Impersonators grows, the food consumed grows not merely with the size of the population, but additionally with the relative age. This has the effect of creating a shortage of sustenance for Elvis Impersonators.

Furthermore, it's unclear how Elvis Impersonators reproduce. Some research suggests the presence of so-called Elviras -- Female Elvis. Consider this female impersonator and the Hitchhiker's Guide to the Galaxy entry. Assuming that Elvis Impersonators reproduce only with females of their own kind (or, possibly, some members of the genetically similar species of Homo sapiens sapiens), it's possible the number of breeding opportunities has gone down.

In conclusion, the species of Elvis Impersonators seems to be on the rise. Large concentrations regularly appear at venues vying for supremacy, the popularity of Las Vegas clubs, and name recognition is strong. Furthermore, they seem to have advanced into other avenues of entertainment. Consider reports of the popular music band, the Red Elvises. They not only give frequent concerts, but have even been featured in a motion picture. Additionally, there is a troupe of skydiving Elvis Impersonators. Indeed, they've shown a remarkable ability to adapt despite a lack of new source material, crossing international boundaries. While pressures mount, it's likely that the population will be able to bear it and continue growing into a mature species, for better or worse.