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 5552 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.
(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.
How old is the Shroud of Turin, according to these data?