My favourite function…

The content of this post originally appears on Chalkdust’s ‘What’s your favourite function? Part II’ post.

Rob Beckett’s favourite is a classic:

e^x

My favourite function is the exponential function f(x)=e^x. This is primarily because \frac{d}{dx}(f(x))=e^x, in other words the function is growing at a rate which is equal to its current size. This is a really interesting property which comes from the fact that e=\lim\limits_{n\rightarrow \infty}{(1+\frac{1}{n})^n}. Just like pi is the ratio between the circumference and diameter of circles, the number e is the base rate of growth and it crops up whenever things grow or decay continuously and exponentially. Our exponential function appears when considering bacterial growth rates, populations, radioactive decay and even occurs in the Black-Scholes formula which is used in the financial market.