Carbon-14 is a radioactive isotope of carbon found in all living organisms. While the organism is alive, carbon-14 is continually restored to maintain a roughly constant amount. When the organism dies, however, carbon-14 begins to decay into more common isotopes of carbon. The rate of decay of carbon-14 is proportional to the amount currently present, with a positive constant of proportionality k. a) If y is the amount of carbon-14 present in a dead organism then y satisfies the differential equation: dy -ky dt g years 1 (hint. your answer may contain the variables y, t and/or the positive constant k. Since carbon-14 decays over time one would expect the rate of change to be negative.) b) Given that the half life of carbon-14 has been experimentally determined to be approximately 5710 years, determine the value of k. Give your answer correct to at least 6 decimal places. k = 0.000121 years -1. c) In 2007 a baby wooly mammoth carcass was found buried in the permafrost in northern Russia. Via a chemical analysis, it was found that the carcass contained approximately 1.1%% of the carbon-14 assumed to be present in an actual living woolly mammoth. How old was the carcass? Give your answer correct to at least the nearest year. 37272 years. Submit Answers