Exponential Functions Equation

Actually Noah... this brings up an interesting point... Should we NOT count this as continuous growth? I thought we should because this is a population growth problem, thus I used the continuous growth model. But you used the non continuous exponential growth model that is usually used for things like interest which is applied only once in a given period:



(Granted, you used geometric series... but that gives you the non continuous result)

Short answer is already answered by Russt.

Long answer is that we should never, if a question is asked like this, integrate like that. This is actually not continuous growth, and we have to treat it as such. So, in fact, doing integration actually gives you the wrong answer (url). That's because, in your case, you don't think of it as growth over one month but rather that the increase by a percentage for every dt. Δy for any given t to t+1 should thus be 1.04/1.03, but yours grow faster because it includes the area between the diff to calculate the growth: 1 and 2.

Geometric series works perfectly well for continuous series as well, by the way.

Noah