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The Shroud of Turin is a religious artifact, claimed by some to be the burial cloth...

The Shroud of Turin is a religious artifact, claimed by some to be the burial cloth of Jesus of Nazareth. The first historical references to the Turin Shroud date from the mid-1300s AD. A team of scientists was permitted to use Carbon-14 dating to estimate the date of the creation of the Turin Shroud in 1988 AD. Analyses found that the amount of Carbon-14 in the shroud was 91.88% of what would be found in a living flax plant, the plant used to make the linen for the Turin Shroud. Carbon-14 is only absorbed while a plant is living, so the linen in the Turin Shroud had 100% of its Carbon-14 at the time the shroud was made. The half-life of Carbon-14 is 5730 years.

(a)Find a model R(t) for the proportion of Carbon-14 remaining in the Turin Shroud as a function of time t in years since the Turin Shroud was created.

(b) (10 points) If the Turin Shroud dated from 33 AD1, what proportion of the initial Carbon-14 would the shroud still have in 1988 AD? You do not need to simplify your answer.

(c) (10 points) Determine an estimate for the year the Turin Shroud was created using the proportion of Carbon-14 remaining in 1988 AD. Simplify your answer and give the year in terms of the Gregorian calendar, e.g. AD or BC. 1The accepted date for the death of Jesus of Nazareth.

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