Originally posted by Bardock42
Anyways, dadudemon and I talked about the silly question the thread starter posted, and he was going to do the maths, but apparently didn't yet, so imma go do it and you guys may tell me where I went wrong.
HEY! You and I agreed that the calculation would be almost unusable due to the social variables that would change the relative rate. 😠 😠
But, the formula was really simple, so, it was no biggie.
Originally posted by Bardock42
So, first we are going to take the land mass of the earth from wikipedia....that's a nice and small 148,940,000 km².Now, we'd rather have it in m² cause that's less hard on the old brain. So we add 6 zeros, cause 1 km² is 1,000,000m², aight?
Awesome, so earth's land mass is 148,940,000,000,000m²
We agreed that a person standing up needs about 0.2m² standing space, I think he heard on TV once someone estimating a packed gathering with 2 square feet, but that's close enough. And it makes calculating that much easier. So anyways to fill the whole land mass of earth we'd need 5 people per m² so
Yup. So far, so good. And, it was a "government" number where they were measuring how many protesters were packed in an area by the Washington Monument. It's pretty reasonable. FYI, KMC peeps, it was actually 2ft² which comes to about .185m²...but we rounded up to .2m² because Bardock joked that Germans are fatter these days. 😆 (Americans are definitely fatter these days so they deserve the boost up to .2m²)
Originally posted by Bardock42
148,940,000,000,000 * 5 = 744,700,000,000,000 people. Everyone with me?
You probably need to explain the where you got the number 5 from: 5 comes from the reciprocal of .2m²...which would be 5 over 1...because you have to multiple by the inverse in order to get the "people per unit area" because you want 1 to be the denominator. Hard to explain...but consider it a conversation factor or something silly.
Damn, talking in circles...
Basically, how many people can fit into one square meter? If ONE person fits into .2m²...then FIVE people can fit into an area five times that large which happens to be 1m².
Make sense? I hope so. 🙁
Originally posted by Bardock42
Now dadudemon figured this to be a easily solvable equation which would pretty closely show the population increase per year. and I do agree that it is sufficient:Final Population = Current Population * (1+birth rate)^time in years.
So we solve for the power
Final Population/Current Population = (1+Birth Rate)^time in years
(ln(Final Population/Current Population))/ln(1+Birthrate)=time in years
Birth rate is around 2% I believe. Death rate won't matter. This assumes that the immortal beings all can have children forever and want them...at the same rate we want them now. If that was not the case I believe the model would be very similar to what it is now in real life, since "death" would be exchanged for "infertility due to age" so I suppose you can look that up and make some calculations based on current numbers, I won't though.
Anyways, the calculation is
(ln(744,700,000,000,000/7,000,000,000)/ln(1+0,02) = t
ln(106386)/ln(1.02)=t
11,57/0.02=t
578,5 = t
So it would take 578.5 years! Sounds plausible? Any problem with the calculation? Played too fast and loose with the decimals?
Here's his math explained step by step, and solved using log instead of ln...with some algebraic simplification to keeps thinks easy to "mess with":
FP/CP = (1+r)^t
Where FP is final population, CP is current population,
r is rate of change, and t is time in years.
Replace your variables with your values:
744,700,000,000,000 = 7,000,000,000 * (1 + .02 ) ^ t
First, you must isolate t with simple algebra so
divide each side by 7 billion:
744,700,000,000,000/7,000,000,000 =7,000,000,000/7,000,000,000 (1+ .02)^t
Then, simplify each side and round to the nearest hundred thousandth:
106385.71428 = (1 + .02)^t
Now, use logorithms to solve for t:
log of 106385.714 base 1.02 = t
Since we will be using a regular calculator and not
a scientific one, we have to solve that using a base 10
log like so
logarithm base y (x) = log(x)/log(y)
that comes to...
logarithm base 1.02 (106385.71428) = log(106385.71425)/log(1.02)
That equals 584.50964
So, 585.5 years.
We could be sticklers for decimal places to adhere to the "scientific accuracy decimal places rule"...but naaaaah.
In other words, Bardock42, your numbers are correct and you did everything correctly. (Did you even doubt that? awesome )
Originally posted by Bicnarok
Maybe nature has a built in security valve for when a race gets too populious, ie releasing some nasty ass disease, letting a few mega volcanoes like in Yellowstone (or the other one) & the Eifel in Europe.Not to mention the human built in " lets start a war " effect that comes up very often.
😆 😆 😆
What a shitty way to go: ass disease!
😆
Alright, alright, I'm done...honest.