The ratio of carbon-14 to carbon-12 in a prehistoric wooden artifact is measured to be one-eight of the ratio measured in a fresh sample of wood from the same region. the half life of carbon-14 is 5,715 years. determine its age.

Carbon-14 is radioactive and decays spontaneously. Interaction between stellar radiation and atmospheric nitrogen ensures a constant carbon-14 to carbon-12 ratio in the earth atmosphere. Living plants undergo respiration and take in carbon constantly and maintain a constant carbon-14-to-carbon-12 ratio in their tissues. Carbon atoms in wood artifacts are no longer refreshed such that the relative abundance of carbon-14 decays exponentially.

It takes one half-life for the relative abundance of carbon-14 in a sample to drop by one half. It would thus take three consecutive half-lives for the mass of carbon-14 in the wooden artifact to decrease by a factor of eight.

as seen in the question. Three half-lives would thus correspond to

The age of this sample is therefore at most.

because natural gas is colorless, odorless, and tasteless, distributors add mercaptan (a chemical that smells like sulfur) to give natural gas a distinct unpleasant odor (it smells like rotten eggs). they locate the types of rock that are likely to contain natural gas deposits.