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 5566 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 Cr KC. (b) In 1988 three teams of scientists found that the Shroud ofTurin, 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[ij. How old is the Shroud of Turin, according to these data? Age years [11: The New York Times, October 18, 1988.