The Shroud of Turin is a religious artifact, claimed by some tobe the burial cloth of Jesus of Nazareth. The first historicalreferences to the Turin Shroud date from the mid-1300s AD. A teamof scientists was permitted to use Carbon-14 dating to estimate thedate of the creation of the Turin Shroud in 1988 AD. Analyses foundthat the amount of Carbon-14 in the shroud was 91.88% of what wouldbe found in a living flax plant, the plant used to make the linenfor the Turin Shroud. Carbon-14 is only absorbed while a plant isliving, so the linen in the Turin Shroud had 100% of its Carbon-14at the time the shroud was made. The half-life of Carbon-14 is 5730years.
(a)Find a model R(t) for the proportion of Carbon-14 remainingin the Turin Shroud as a function of time t in years since theTurin Shroud was created.
(b) (10 points) If the Turin Shroud dated from 33 AD1, whatproportion of the initial Carbon-14 would the shroud still have in1988 AD? You do not need to simplify your answer.
(c) (10 points) Determine an estimate for the year the TurinShroud was created using the proportion of Carbon-14 remaining in1988 AD. Simplify your answer and give the year in terms of theGregorian calendar, e.g. AD or BC. 1The accepted date for the deathof Jesus of Nazareth.
