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: .. _y : g yearsil. dt (hint. your answer may contain the variables y, t and/or the positive constant k. Since carbon14 decays over time one would expect the rate of change to be negative.) b) Given that the half life of carbon14 has been experimentally determined to be approximately 5740 years, determine the value of k. Give your answer correct to at least 6 decimal places. E k = I years1. 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 yeah years