K Concentration on Earth Over Time

[ilona]

Homework Statement

Hei!Half life of the reaction is about 1,25 billion years. Assuming that the age of Earth is 5 billion years,the concentration of K on Earth since its formation decreased:
a)2times b)4times c)8 times d)16times

The Attempt at a Solution

So I just do like that T$\underline{}1/2$=1,25 bilion years
age=5 bilion years
so in the beginning we have X and then it is X/2 so we 1,25 bilion year
then X/4 it is 2,5 bilion year and then X/8 so it is 5 bilion years
so the answer i think is it decreased 8 times
but my question is: is there easier way to do it?

thanks in advance!

 

[Borek]

After half life you are left with $\frac 1 2$ of the initial amount, after two half lives you are left with half of that or $\frac 1 2 \times \frac 1 2 = (\frac 1 2)^2$ of the initial amount, after three half lives you are left with half of that or $(\frac 1 2)^3$ of the initial amount and so on.