A piece of cloth is discovered in a burial pit in the southwestern United States. A tiny sample of the cloth is burned to CO₂, and the ¹⁴C/¹²C ratio is 0.250 times the ratio in today’s atmosphere. How old is the cloth?

Strategy 

We have the decay constant, k, for the relevant process from Example Problem 14.4. This will allow us to determine t, the time that has passed since the fiber in the cloth was harvested.