In words, this is: if the rate of change of a thing is proportional to the thing itself, what is the thing, and how does it actually change with time? Similar situations occur all over the place, and not just in biology and physics.įrom a mathematical point of view, there is a problem, an equation, to solve in all these situations.

The same logic applies to any particle decay, even the exotic ones we produce at Cern with at the Large Hadron Collider. Radioactive decay is exponential because the number of atomic nuclei breaking up at a given moment is proportional to the number of nuclei that actually exist at that moment. Population growth can be exponential because the number of new people (or bugs, or bacteria) being produced at a given time is proportional to the total number of people (bugs, bacteria) around at that time. True exponential increases and decreases occur whenever the rate of change of something is proportional to the thing itself.

But exponentials are really interesting, and are very common even in the precise mathematical sense. I'm not being pedantic about it, that's not the point (and don’t get me started on what “hyperbolic” really means, mathematically). It means - according to the way the Romans executed one in 10 soldiers as a punishment - destroying 10% of something, but is often used as a hyperbolic description of an even more damaging event. It's rather common for terms which have a precise mathematical meaning to be used loosely for the purposes of emphasis.

Other words for exponent in math