4052 years old.
25% is half of half life. so 2 to the .5 of a half life.
So the amount of the carbon left. is
The sample is 2380 years old.
We can express the rate law for a first-order decay as
We can rewrite this as
If the concentration of carbon-14 has decreased by 25 %, then 75 % remains.
The sample has decayed for 0.4150 half-lives.