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On 2012, Feb 05, , at 12:26, John Denker wrote:
3) More generally: For any X that is an exponential function of t,
calculate É¢X/É¢t for any fixed finite É¢t ... 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
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.