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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 5545 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 Off- -kC (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 was old the Shroud of Turin in 1988, according to these data? Age = years [1] The New York Times, October 18, 1988