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Geometric Progressions

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Geometric Progressions

Postby flipper1067 » Mon Aug 27, 2007 3:33 am

This is a thought producing question in my text book:

What is the effect of reducing the constant factor by which the geometric progression increases? Might this effect be achieved with humans? How?

I was curious what people had for answers.
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Postby david23 » Mon Aug 27, 2007 6:35 am

Is the progression of human population geometric?
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Postby kotoreru » Mon Aug 27, 2007 9:38 am

Let me get this right before I wade in: geometric growth is the same as expoential, yes? i.e. 1,2,4,8,16, 32.

I cant remember the name of the other type i.e. 1,2,4,6,8,10.

Wait, I could have that mixed up. Possibly the second one is geometric as it increases with a constant of 2.

Er, in that case reducing the constant would slow the population rate, without considering death in the population. I could be vastly confused.
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Postby flipper1067 » Mon Aug 27, 2007 12:20 pm

There is also an arithmetic growth which grows by 2 (2, 4, 6, 8, 10), as in producing food. In my book, the geometric growth is a factor of 3 (3, 6, 18, 54). So, it sounds like they are asking me how to decrease the geometric growth of population. And how? (If it can be done). Besides not letting people have as many children, or people dying younger, I am not sure how you would change that?
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Postby AstusAleator » Mon Aug 27, 2007 11:53 pm

eat the poor


JUST KIDDING

I could be misunderstanding the question, but I think that population growth with humans can be impacted largely by culture. If a society has a culture that encourages the use of contraceptives, and discourages having lots of children, then you'll likely see population growth stabilize.
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Postby mith » Tue Aug 28, 2007 2:45 am

In terms of comparison, reduction of the constant factor has limited use because in the end the geometric will always win out. But I guess you could sorta shift it so that it remains at the long tail end of the graph longer...

You can also slow geometric growth by lowering the initial amount of people you have. This can be easily accomplished by not paying to maintain the dams in certain hurricane susceptible states and by having wars.
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Postby flipper1067 » Tue Aug 28, 2007 3:06 am

Ok, so....Eat the poor, encourage wars, don't maintain the dams, and.....Don't treat diseases!
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Postby alextemplet » Tue Aug 28, 2007 5:42 am

flipper1067 wrote:Ok, so....Eat the poor, encourage wars, don't maintain the dams, and.....Don't treat diseases!


And don't forget to use the death penalty very liberally as well!
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Postby kotoreru » Tue Aug 28, 2007 12:14 pm

Ha! This thread just reminded me of an anecdote I read somewhere:

If we remove limiting factors, then assume that each pair of humans has 1 offspring who goes on to create 1 offspring with 1 other - no death except for old age - then in 500 years we would have a mass of humanity moving outwards from Earth at the speed of light.

I just like the term 'mass of humanity'. Sounds like a band or something.

I could have omitted something here or got it wrong somewhere, but that's the gist of it. And yes, please disregard common sense for things like space, air and other so called "essentials".
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Postby AstusAleator » Tue Aug 28, 2007 3:23 pm

kotoreru are you saying that every pair of parents producing one child would cause population increase?
I'm fairly certain it would in fact decrease the population.

Start with population 50, all same age, 1/2 male 1/2 female. Assume offspring are born 1:1 male/female. Lets say human lifespan is 3 generations.

Generation 1: total population 50

Generation 2: (50 + (50/2*1)) total population: 75

Generation 3: (75 + (25/2*1)) total population: 87.5 *round down to 87*

Generation 4: (87 + (12/2*1) - 50) total population: 43

Generation 5: (43 + (6/2*1) - 25) total population: 21

Generation 6: (21 + (3/2*1) - 12) total population: 10

Generation 7: (10 + (0) - 6) total population: 4

Generation 8: (4 + (0) - 3) total population: 1

Generation 9: (1 + (0) - 1) total population: 0


Ok that was all probably self explanatory but I had fun writing it all up so... yeah.
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Postby alextemplet » Tue Aug 28, 2007 5:09 pm

No, I understood it, Astus. I'm glad you had fun. Perhaps it was meant to be every couple produces two offspring? Then, if a person survived three generations, s/he would have six descendants (two children and four grandchildren) before death.
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Postby kotoreru » Tue Aug 28, 2007 5:14 pm

Yes, I'm fairly sure I left out the repetitions in there somewhere i.e. each pair producing 1 offspring every 3 years or something. D'oh!

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