1. The half-life of polonium-210 is 138.4 days. How many milligrams of polonium-210 remain after 415.2 days if you start with 2.0 mg of the isotope?

Okay so if the half like is 138.4 days, the mass of polonium will half every 138.4 days.

We need to work out how many half lives are in 415.2 days so we do 415.2/ 138.4 to get 3

This means the mass will half 3 times so you do

2.0/2/2/2
Or 2.0/2^3
Which gives 0.25

So 0.25mg will remain after 415.2 days

Hope this helps, let me know if you have any questions