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Carbon-14 is a radioactive isotope used to date objects. If A0 represents the initial amount of...

Carbon-14 is a radioactive isotope used to date objects. If A0 represents the initial amount of carbon-14 in the object, then the quantity remaining at time t, in years, is A(t) = A0e^−0.000121t .

(a) A tree, originally containing 185 micrograms of carbon-14, is now 500 years old. At what rate is the carbon-14 decaying now?

(b) In 1988, scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of carbon-14 in freshly made cloth of the same material. According to this data, how old was the Shroud of Turin in 1988?

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