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 5550 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 was old the Shroud of Turin in 1988, according to these data?
Age = years

[1]: The New York Times, October 18, 1988.