Math help
Post Reply
 
Thread Rating:
  • 0 Votes - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
13-01-2015, 01:48 PM
Math help
I am a bit rusty on exponentials and algebraic problems. I’m trying to determine what the population of the earth would be if 8 people grew at 2% (2% is a bit above our current average) for 6,000 years. This site shows me how to do the math and still I’m not getting the answer.

http://www.coolmath.com/algebra/17-expon...wth-01.htm

So what we really need is to solve for the growth rate of 8 people to become 7.1 billion in 6,000 years! I’m curious, thanks for your help.

P = ?

Po = 8e
r = 0.02
t = 6000

and

r = ?
Po = 8e
P = 7,100,000,000
t = 6000

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
Find all posts by this user
Like Post Quote this message in a reply
13-01-2015, 01:51 PM
RE: Math help
http://www.worldometers.info/world-population/

"At the dawn of agriculture, about 8000 B.C., the population of the world was approximately 5 million. Over the 8,000-year period up to 1 A.D. it grew to 200 million (some estimate 300 million or even 600, suggesting how imprecise population estimates of early historical periods can be), with a growth rate of under 0.05% per year.”

So if the flood killed the 5 million 2000 years before the earth was created Facepalm what would the population growth have to be to reach 7.1B in 6000 years?

Simple question. Big Grin

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
Find all posts by this user
Like Post Quote this message in a reply
13-01-2015, 02:42 PM
RE: Math help
(13-01-2015 01:51 PM)Full Circle Wrote:  http://www.worldometers.info/world-population/

"At the dawn of agriculture, about 8000 B.C., the population of the world was approximately 5 million. Over the 8,000-year period up to 1 A.D. it grew to 200 million (some estimate 300 million or even 600, suggesting how imprecise population estimates of early historical periods can be), with a growth rate of under 0.05% per year.”

So if the flood killed the 5 million 2000 years before the earth was created Facepalm what would the population growth have to be to reach 7.1B in 6000 years?

Simple question. Big Grin

So we're starting with 8 right? And we're assuming exponential is a decent model.

OK so it's gonna be P_0*R^T = P and we know P_0 is 8 and T is 6000 years and P is 7.1 bn

So P / P_0 = R^T and taking logs both sides...

log (P / P_0) = T log R

log R = log(P/P_0)/T = 0.00149136139362118861674193545848

R = 1.0034

So year on year you need an extra population of 0.34% - R includes 1 as the original pop + the extra is the growth.

We'll love you just the way you are
If you're perfect -- Alanis Morissette
(06-02-2014 03:47 PM)Momsurroundedbyboys Wrote:  And I'm giving myself a conclusion again from all the facepalming.
Find all posts by this user
Like Post Quote this message in a reply
[+] 1 user Likes morondog's post
13-01-2015, 02:59 PM (This post was last modified: 13-01-2015 03:05 PM by morondog.)
RE: Math help
For the second bit

P = P_0 * R^T

Plug it into calculator...

[edit: made some calc mistakes]
[edit: got it right the first time Facepalm]

8 * 1.02^6000 = 3.19 x 10^52 people.

That's a lotta humans. The mass of the Earth (from wikipedia) is 5.97219 × 10^24 kg. So if each human weighs 50 kg there'll be enough mass for 267274143727698246160713453077 Earths.

The Chandrasekhar limit for the point at which a mass becomes a black hole is 2.765 × 10^30 kg so by mere fucking, in 6000 years and with exponential growth, we could give ourselves a lot more problems than simply global warming Big Grin

We'll love you just the way you are
If you're perfect -- Alanis Morissette
(06-02-2014 03:47 PM)Momsurroundedbyboys Wrote:  And I'm giving myself a conclusion again from all the facepalming.
Find all posts by this user
Like Post Quote this message in a reply
[+] 4 users Like morondog's post
13-01-2015, 03:26 PM
RE: Math help
(13-01-2015 02:42 PM)morondog Wrote:  
(13-01-2015 01:51 PM)Full Circle Wrote:  http://www.worldometers.info/world-population/

"At the dawn of agriculture, about 8000 B.C., the population of the world was approximately 5 million. Over the 8,000-year period up to 1 A.D. it grew to 200 million (some estimate 300 million or even 600, suggesting how imprecise population estimates of early historical periods can be), with a growth rate of under 0.05% per year.”

So if the flood killed the 5 million 2000 years before the earth was created Facepalm what would the population growth have to be to reach 7.1B in 6000 years?

Simple question. Big Grin

So we're starting with 8 right? And we're assuming exponential is a decent model.

OK so it's gonna be P_0*R^T = P and we know P_0 is 8 and T is 6000 years and P is 7.1 bn

So P / P_0 = R^T and taking logs both sides...

log (P / P_0) = T log R

log R = log(P/P_0)/T = 0.00149136139362118861674193545848

R = 1.0034

So year on year you need an extra population of 0.34% - R includes 1 as the original pop + the extra is the growth.

So 0.34/0.05 = about 7 times greater than historical average if I read that page right.

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
Find all posts by this user
Like Post Quote this message in a reply
13-01-2015, 03:30 PM
RE: Math help
(13-01-2015 02:59 PM)morondog Wrote:  For the second bit

P = P_0 * R^T

Plug it into calculator...

[edit: made some calc mistakes]
[edit: got it right the first time Facepalm]

8 * 1.02^6000 = 3.19 x 10^52 people.

That's a lotta humans. The mass of the Earth (from wikipedia) is 5.97219 × 10^24 kg. So if each human weighs 50 kg there'll be enough mass for 267274143727698246160713453077 Earths.

The Chandrasekhar limit for the point at which a mass becomes a black hole is 2.765 × 10^30 kg so by mere fucking, in 6000 years and with exponential growth, we could give ourselves a lot more problems than simply global warming Big Grin

This assumes no one is dying right?

“I am quite sure now that often, very often, in matters concerning religion and politics a man’s reasoning powers are not above the monkey’s.”~Mark Twain
“Ocean: A body of water occupying about two-thirds of a world made for man - who has no gills.”~ Ambrose Bierce
Find all posts by this user
Like Post Quote this message in a reply
13-01-2015, 03:44 PM
RE: Math help
Actually, assuming people do not reproduce with a probability of 2 % on the same day of the year as an annual exercise (lol) you should be using exponential growth equations.

N=N_0 * e ^ (r * t)

Where N_0 is the original number of people, r is the rate of reproduction ( .02 / year) and t is in years.

I get 1.04 * 10^53
Find all posts by this user
Like Post Quote this message in a reply
13-01-2015, 03:47 PM
RE: Math help
(13-01-2015 03:30 PM)Full Circle Wrote:  
(13-01-2015 02:59 PM)morondog Wrote:  For the second bit

P = P_0 * R^T

Plug it into calculator...

[edit: made some calc mistakes]
[edit: got it right the first time Facepalm]

8 * 1.02^6000 = 3.19 x 10^52 people.

That's a lotta humans. The mass of the Earth (from wikipedia) is 5.97219 × 10^24 kg. So if each human weighs 50 kg there'll be enough mass for 267274143727698246160713453077 Earths.

The Chandrasekhar limit for the point at which a mass becomes a black hole is 2.765 × 10^30 kg so by mere fucking, in 6000 years and with exponential growth, we could give ourselves a lot more problems than simply global warming Big Grin

This assumes no one is dying right?

That 2% would be a reasonable rate taking into account death rates. In my above post, if say the birth rate was 3% and death rate was 1%, the exponential would be (r_birth - r_death) * t . Of course plagues, wars, and the like means reality is not a smooth exponential.
Find all posts by this user
Like Post Quote this message in a reply
13-01-2015, 04:05 PM
RE: Math help
(13-01-2015 03:44 PM)BryanS Wrote:  Actually, assuming people do not reproduce with a probability of 2 % on the same day of the year as an annual exercise (lol) you should be using exponential growth equations.

Mmm, good point.

We'll love you just the way you are
If you're perfect -- Alanis Morissette
(06-02-2014 03:47 PM)Momsurroundedbyboys Wrote:  And I'm giving myself a conclusion again from all the facepalming.
Find all posts by this user
Like Post Quote this message in a reply
13-01-2015, 04:07 PM
RE: Math help
(13-01-2015 04:05 PM)morondog Wrote:  
(13-01-2015 03:44 PM)BryanS Wrote:  Actually, assuming people do not reproduce with a probability of 2 % on the same day of the year as an annual exercise (lol) you should be using exponential growth equations.

Mmm, good point.
Also, the new people are going to take around 20-30 years before they start reproducing and at about 38 years they are generally done, certainly past 50 years not many keep reproducing.
Find all posts by this user
Like Post Quote this message in a reply
Post Reply
Forum Jump: