Aliving specimen in equilibrium with the atmosphere contains one atom of 14c (half-life = 5730 yr) for every 7.7 ✕ 1011 stable carbon atoms. an archeological sample of wood (cellulose, c12h22o11) contains 22.2 mg of carbon. when the sample is placed inside a shielded beta counter with 88.0% counting efficiency, 811 counts are accumulated in one week. assuming that the cosmic-ray flux and the earth's atmosphere have not changed appreciably since the sample was formed, find the age of the sample.