The radioactive isotope carbon 14 is present in small quantities in all life forms and it is constantly replenished until the organism dies after which it decays to stable carbon 12 at a rate proportional to the amount of carbon 14 present with a half life of 5699 years Suppose C t is the amount of carbon 14 present at time t a Find the value of the constant k in the differential equation C kC k b In 1988 three teams of scientists found that the Shroud of Turin which was reputed to be the burial cloth of Jesus contained about 91 percent of the amount of carbon 14 contained in freshly made cloth of the same material 1 How old is the Shroud of Turin according to this data Age years 1 The New York Times October 18 1988