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.
Where:
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.