Re: [Phys-l] scope of the course

[chuck britton <cvbritton@mac.com>]

Proofs? Do algebra based courses require proofs? 
Fifth grade courses certainly don't.

Any course in science that uses percentages 
should include exponential growth/decay and 
should include the rough approximation that 
relates growth rate (% / time) and half-life.

I've heard bankers call this the 'Rule of 72' 
since 72 has many factors that used to be equal 
to 'reasonable' % interest rates.

This 'rule' is only good for small percentages 
but has enough usefulness to be taught and used 
much more than it is currently.
.
At 1:00 PM -0800 2/5/12, Bernard Cleyet wrote:
> On 2012, Feb 05, , at 12:26, John Denker wrote:
>
> >  3) More generally:  For any X that is an exponential function of t,
> >  calculate ɢX/ɢt for any fixed finite ɢt ... not necessarily equal to
> >  the half-life.  No need to take the limit dX/dt; finite differences
> >  work just fine.  Observe that the rate of change in X is proportional
> >  to X.
>
>
> OK, this works, but just the graph doesn't, as 
> unless the range is sufficient, a power law or 
> even quartic, etc. looks like an exponential.  I 
> just used the model function in Graphical 
> analysis to check this.
>
> Of course, once one has plotted, say growth, one 
> may use GA to fit various functions to discover 
> it is indeed exponential.
>
>
> For decay.  I before using a short (~ one 
> minute) half life source give the exercise of 
> one thousand dice removing the ones after each 
> throw.  This also shows the scatter, especially 
> if ten groups throwing initially 100 and then 
> successively combining their results.  One may 
> apply, approximately, the Poisson distrib. to 
> this too.
>
> Not incidentally, graphing is not proof?   Is the differential eq. proof?
>
> bc wonders if graphing is derivation.