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 dt 9 years 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 5730 years determine the value of k Give your answer correct to at least 6 decimal places k years 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 years