Why do we use the constant 'e' when describing the half life (decay) of elements?

[syncmaster913n]

Whenever the half life is mentioned, I see it presented in terms of 'e'. For example, if the half life of an element is 30 years, and we wanted the formula for the decay, assuming 100 grams of the elements, I will usually see the following in books and online:

100 / e^ln(2)/30*x

(x is number of years)

I was wondering if there was a specific reason why we don't just use the number 2 instead? So:

100 / 2^x/30

It looks both cleaner and more intuitive as to what it is representing. Could someone explain to me the advantage(s) of using the former?

 

[stapel]

Whenever the half life is mentioned, I see it presented in terms of 'e'. For example, if the half life of an element is 30 years, and we wanted the formula for the decay, assuming 100 grams of the elements, I will usually see the following in books and online:

100 / e^ln(2)/30*x

(x is number of years)

I was wondering if there was a specific reason why we don't just use the number 2 instead? So:

100 / 2^x/30

It looks both cleaner and more intuitive as to what it is representing. Could someone explain to me the advantage(s) of using the former?

At this point in your studies, it probably wouldn't make much difference which base is used; some books do prefer a base of 2. However, when you get to calculus, they'll explain why "e" is so much nicer.