In 1389, Pierre d’Arcis, the bishop of Troyes, wrote a memo to the pope, accusing a colleague of passing off “a certain cloth, cunningly painted,” as the burial shroud of Jesus Christ. Despite this early testimony of forgery, the image on the cloth is so compelling that many people regard it as a sacred relic. Known as the Shroud of Turin, the cloth was subjected to carbon dating in 1988. If authentic, the cloth would have been approximately 1,960 years old at that time.

a. If the Shroud were actually 1,960 years old, what percentage of the ¹⁴C would have remained?

b. Scientists determined that 92.3% of the Shroud’s original ¹⁴C remained. Based on this information alone, what was the likely age of the Shroud in 1988?