The "Shroud of Turin" caused a great deal of controversy during the decades 1960-80. People argued whether the cloth of the shroud, and the peculiar image of a face imprinted on it, dated from biblical times (around 0 A.D.), or whether it was a forgery created in medieval times (say 1000 A.D.). Finally, religious authorities allowed scientists to test a few square centimeters of the cloth by carbon-14 dating methods. (They had to burn the cloth to do this.) Tests conducted in 1985 reported that: The fraction of 14C remaining in this cloth was 0.877 (about 87.7% of the 14C present when the cloth was formed remained in 1985). The half-life of 14C is T = 5730 years.

(a) What explicit Decay Model predicts the fraction of 14C re- maining in terms of the number of years t that have elapsed since the cloth was woven?

(b) When the tests were conducted, how old was the cloth sam- ple? In what year AD was the shroud made?

(c) Is the shroud a genuine artifact from biblical times? 0