## Math 101: Calculus I

# Carbon-14 Dating

### The Lascaux Cave Paintings

The above images are from H. W. Janson, *History of Art* (Abrams
1991).
Janson gives the date of these paintings as 15,000-10,000 B.C.

### The Shroud of Turin

Positive image of the Shroud (1933)

Negative image of the Shroud (1933)

These images are from the web site of the
Holy Shroud Guild.
The shroud was first exhibited in France in the 1350's.

Problems
Use 5530 years for the value of the half-life in the following problems.
(According to *Radiocarbon dating* by Sheridan Bowman (British
Museum Publications, 1990), the currently accepted half-life for
Carbon-14 is 5530 years. However, the value of 5568 years was given
in the 1940's by Willard Libby and this is the value commonly used
today despite the fact that there are better estimates available;
apparently it's too confusing to have two values for the half-life,
and results are corrected to reflect the true value of 5530 years.)

1. In 1950, a Geiger counter recorded about 1.68 disintegrations per
minute per gram of carbon from some charcoal fragments found in the cave
at Lascaux. For living wood (eg in a tree) the number of
disintegrations is about 13.5 per minute per gram of carbon. Estimate
the age of the charcoal fragments at Lascaux (and hence the age of the
paintings). (From *Modeling and Visualization with ODE Architect*
by R. Borrelli and C. Coleman)

2. Tests done on the Shroud of Turin in 1989 found that it contained 92
percent of its original fraction of Carbon-14. What does this say about
the age of the shroud? (From *Conversational Calculus*
by D. Cohen and J. Henle)

3. Carbon from wood remains found in 1965 in a hole at Stonehenge
contained 62.2 percent of the original fraction of carbon-14. Estimate
the date at which this part of Stonehenge was built. (From W. Durfee:
*Calculus and Analytic Geometry*, p. 357)