Question

Suppose a laboratory has a 30 g sample of polonium-210. The half-life of polonium-210 is about 138 days How many half-lives of polonium-210 occur in 1104 days? How much polonium is in the sample 1104 days later?

Answer 1

the simplified answer is 0.12 g

Answer 2

This is an easy half-life calculation because it involves an exact integer of half-lives.  1,104 days is precisely 8 half-lives.  After each half-life, one half of the original remains.
So, after 8 half-lives you will have 1 / 2^8 of the original material left.
So we start with 30 grams and 1 / 2^8 = 0.00390625.
We are therefore left with (30 * 0.00390625) or 0.1171875 grams of the original 30 grams of polonium.