Question

What fraction of a sample of cobalt-60 (half-life = 5 years) will remain after 25 years?

Answer 1

Let's assume you start with 100 grams.
(Incidentally, the half-life of cobalt 60 which is 5.2714 years (wikipedia))
But we'll stick with 5 years.
According to the formula here:
http://www.1728.org/halflife.htm
Ending Amount = Beginning Amount / (2^n)
where n= number of half lives
In 25 years, cobalt 60 will undergo 5 half-lives.

So, Ending Amount = 100g / 2^5
Ending Amount = 100g / 32
Ending Amount = 3.125 g

So, basically, after 5 half-lives (or 25 years) the amount of cobalt 60 remaining is .03125 times the original amount.

Answer 2

another way of looking at it is :
\[\large (\frac{1}{2})^{\frac{t}{5}}\]
let t = 25

Answer 3

Okay, that solves it too :-)