Question

A piece of wood found in an ancient city has a carbon-14 to carbon-12 ratio that is one-eighth the carbon-14 to carbon-12 ratio of a tree growing nearby. How old is the piece of wood? (The half-life of carbon-14 is 5,715 years.)

Answer 1

k = 0.693/t_1/2
Substitute k into the below equation.
ln(No/N) = kt
Use 100 for No
Use 12.5 for N (that's 1/8 of 100--or you could simply use 1/8 for that ratio).
k from above.
Solve for t in years.

Answer 2

2865 years