The radioactive isotope radium has a half-life of 1,600 years. the mass of a 100-gram sample of radium will grams after 200 years.

To solve this we are going to use the half life equation 
Where:
is the initial sample
is the time in years
is the half life of the substance
is the remainder quantity after  years 

From the problem we know that:




Lets replace those values in our equation to find :





We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.