Question

An archeological artifact was subjected to radiocarbon dating. The artifact showed a carbon-14 decay rate of 13.8 disintegrations/ min per gram of carbon. Carbon-14 has a half-life of 5715 years, and currently living organisms decay at the rate of 15.3 disintegrations/ min per gram of carbon. What is the approximate age of the artifact.

I know that you need to use the 1st integrated rate law, but how do you find t? Thank you!