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-----Original Message-----_______________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of Ken
Caviness
Sent: Thursday, September 16, 2010 8:57 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] H. Sapiens
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.
/**************************************
"The four points of the compass be logic, knowledge, wisdom and the
unknown.
Some do bow in that final direction. Others advance upon it.
To bow before the one is to lose sight of the three. I may submit to
the unknown, but never to the unknowable." ~~Roger Zelazny, in "Lord
of Light"
***************************************/
________________________________
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 youcan see at:
will probably
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
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
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Ludwik
http://csam.montclair.edu/~kowalski/life/intro.html
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