The age of tzi, the Ice Man, discussed in the chapter introduction, was determined by carbon-14 (14C)

The age of Ötzi, the Ice Man, discussed in the chapter introduction, was determined by carbon-14 (14C) dating. 14C is a radioactive isotope with a half-life of 5730 years. A sample of carbon-containing material was found to have 52.7% of its original amount of 14C. Use this information to calculate how long ago Ötzi lived.
Strategy

Since we want a concentration-time relationship, use the integrated expression for a first-order decay, calculating the rate constant, k, from the half-life. The absolute concentrations are not known, but their ratio is known, because the final concentration is equal to 52.7% of the original concentration.