2043 - The Year That We All Turn Into ELVIS!

We got this great idea from "The Naked Scientist Magazine" issue published December 2000.

Some people who dress as Elvis and sing his songs prefer to call themselves "Elvis Tribute Artists".
But they look like and sound like Elvis impersonators, so we calculate that this makes them into
Elvis impersontator impersonators.

When Elvis Presley died in 1977, it's estimated there were about 170 people impersonating him. This number grew and grew and in the year 2,000 it was estimated there were about 85,000 Elvis impersonators.
Using this information we can calculate the growth factor for Elvis impersonators. If you've read The Perfect Sausage you'll know about the growth formula. We can adapt it to get this formula:

Number of Elvises = pe ^{r t} p = the number of Elvis impersonators in 1977.
e = the growth constant which is 2.718281828...
r = the growth factor (we have to work this bit out)
t = the number of years since 1977.

Normally this formula would be applied to the interest you should earn from having money in the bank. P would be the premium (i.e. the money you start with), r would be the interest rate (usually as a decimal) and t would be the number of years you have the money in for.

The first thing we need to do is work out what r is. We know that the number of impersonators in the year 2000 is 85,000 and we also know that p = 170 so that's all right. The number of years between 1977 and 2000 is 23, so t = 23. We get a little equation:
85,000 = 170 x (2.718281828)^{r x 23}

With a little less conversation, a little more action if you please , we can work out that r = 0.2702005. (In other words the number of Elvis impersonators grows by just over 27% each year.)
Here's the bit that will leave you all shook up...
If you've got a suspicious mind, try working out how many Elvis impersonators there will be in the year 2043. Use the same formula, but put in t = 66 and you can use the value of r we've worked out, because that's the wonder of you.
Here's what the sum looks like:
170 x (2.718281828)^{0.2702005 x 66}

You'll find that the number of Elvis impersonators in 2043 is 9,447,645,907. The population of the Earth in 2043 is expected to be slightly less than this number. So that means EVERYBODY on earth including people in the ghetto will be a guitar man just like Elvis...

...and a few extra Elvis impersonators will have arrived from elsewhere!

WARNING: if the Evil Gollarks are sent down to stay in Heartbreak Hotel wearing their blue suede shoes, then don't be cruel, just return to sender by chasing them off with your hound dog.

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Find out about the growth formula in
THE PERFECT SAUSAGE

Find out about e in
THE KEY TO THE UNIVERSE

Find out about everything in
THE MURDEROUS MATHS OF EVERYTHING

2043 - The Year That We All Turn Into ELVIS!

Number of Elvises = pe r t p = the number of Elvis impersonators in 1977. e = the growth constant which is 2.718281828... r = the growth factor (we have to work this bit out) t = the number of years since 1977.

...and a few extra Elvis impersonators will have arrived from elsewhere!

Number of Elvises = pe ^{r t} p = the number of Elvis impersonators in 1977.
e = the growth constant which is 2.718281828...
r = the growth factor (we have to work this bit out)
t = the number of years since 1977.