If 25.0 g of a radioactive sample is left after 100.0 years and each half-life is 25 years, how much sample did you start with?
At the end of 1 half life (25 years) you would have (1/2)*X = what's left(25)
At the end of two half lives (50 years) you would have (1/4)*X = 25
At the end of three (75 years)...................................(1/8)*X = 25
At the end of four (100 years) half lives...................(1/16)*X = 25
So you must have had 16 * 25 g to start with or 400 grams.
The formula way of doing this is as follows:
k = 0.693/half life = 0.693/25 = 0.0277
Then ln(No/N) = kt
No = solve for this
N = 25.0
k = 0.0277 from above
t = 100 years
ln(No/25) = 0.0277*100
No = 400