Thread: The significance of "e"

Whenever i study differential equations, alot of the questions provide an equation of a specific model of a system at some point in time( particle model, economic model, bacteria growth, radioactive decay, rate of water flow, wind speed, inductance, and impedance etc...). Whenever i solve this in to the desirable form in which the question asks, i notice alot of the forms come in with the mathematical constant "e"

So here is my question, why do alot of things in nature seem to agree with the mathematical constant "e"?

I would say because they were defined to do so. I mean it's in the definition of the natural logarith and e.

e is the unique number that satisfies . Any other number would introduce some multiplier in the right hand side. (Another way of putting that would be the differential equation .)

Originally Posted by MagiMaster

e is the unique number that satisfies . Any other number would introduce some multiplier in the right hand side. (Another way of putting that would be the differential equation .)

yes

What is fundamental is really the finction , the exponential function, properly defined by a poweer series, and not the number .