Re: [Phys-l] H. Sapiens

[Ken Caviness <caviness@southern.edu>]

Ah, the "Rule of 70".  That's sometimes taught in finance, business or economics classes.  I'm not sure why.  Most people can't divide x into 70 without a calculator anyway, and most calculators have an "ln x" button, so it would be basically as quick to use the more exact formula, ln2/r.  And this has the advantage of immediate extensibility to questions such as, "How long does it take for a population increasing at rate x to triple?" -- (ln3/r)

This is just exponential growth, also known as continuously compounded interest, which I was taught to remember using the "pert" formula:  A = P e^(rt), where P is the principal or original number/amount, A is the future amount, t is the time in some convenient units, r is the interest or growth rate (per time unit).  The more standard exponential growth/decay formula is N = N_0 e^(+-r t), sometimes using lambda instead of rate r, but it's the same thing.  

To get the rule of 70, I just plugged in P = 1, A = 2:

A = P e^(rt) ==> 2 = e^(rt) ==> ln2 = rt  ==> t = ln2/r ==> t = ~ 0.693/r = 69.3/(100r) = ~70/x.

Of course, you have to use the decimal for the rate instead of the percentage.  :-)  

So doubling time with a rate of 5.1% per year is ln2 / .051 = ~ 13.6 years.  Using 70/5.1 gives ~ 13.7 years, so the rule of 70 is not bad, just (in my opinion) unnecessary.

Cheers,

Ken

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of curtis osterhoudt
Sent: Thursday, 16 September 2010 1:23 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] H. Sapiens

Remember the simple rule-of-thumb: If something is growing at x% per time y, the doubling time is roughly 70/x to double in y units. That is, a percentage growth rate of (say) 1% leads to a doubling of population in about 70 years. That's _scary_ to me, for _any_ population. 




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________________________________
From: Bernard Cleyet <bernardcleyet@redshift.com>
To: Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu>
Sent: Thu, September 16, 2010 11:15:34 AM
Subject: Re: [Phys-l] H. Sapiens

Contrary to what I presume many think, Mexico is less adding to that problem:

"Throughout most of the twentieth century Mexico's population was characterized by rapid growth. Even though this tendency has been reverted and average annual population growth over the last five years was less than 1%, the demographic transition is still in progress, and Mexico still has a large cohort of youths."

http://en.wikipedia.org/wiki/Demographics_of_Mexico


bc


Demographic transition:

http://anthrocivitas.net/forum/showthread.php?t=1539




On 2010, Sep 11, , at 20:15, ludwik kowalski wrote:

> Actually, I was wrong about the "less than 20 years, as you can see at:
>
> http://en.wikipedia.org/wiki/World_population
>
> Ludwik
>
> = = = = = = = = = = = = = = = = = = = = = = = = = = =
>
> On Sep 11, 2010, at 11:05 PM, ludwik kowalski wrote:
>
> > On Sep 11, 2010, at 10:49 PM, brian whatcott wrote:
> >
> > > There are less than 8 billion people presently on Earth.  . . .
> >
> > This is about four times more than when I was a kid. It will probably 
> > double again in less than 20 years. How can one be optimistic about 
> > the future of sapients?
> >
> >
> > Ludwik
> >
> > http://csam.montclair.edu/~kowalski/life/intro.html
> >
> >
> >
> >
> > _______________________________________________
> > Forum for Physics Educators
> > Phys-l@carnot.physics.buffalo.edu
> > https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
>
> Ludwik
>
> http://csam.montclair.edu/~kowalski/life/intro.html
>
>
>
>
> _______________________________________________
> Forum for Physics Educators
> Phys-l@carnot.physics.buffalo.edu
> https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l

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