Techniques
Island Museum analyzes historical artifacts using one or more techniques described below—all but one of which is performed by an outside laboratory—to obtain specific information about an object's creation. For each type of material listed, the museum uses only the technique described:
Animal teeth or bones: The museum performs isotope ratio mass spectrometry (IRMS) in-house to determine the ratios of chemical elements present, yielding dues as to the animal's diet and the minerals in its water supply.
Metallic ores or alloys: Inductively coupled plasma mass spectrometry (ICP-MS) is used to determine the ratios of traces of metallic isotopes present, which differ according to where the sample was obtained.
Plant matter: While they are living, plants absorb carbon-14, which decays at a predictable rate after death; thus radiocarbon dating is used to estimate a plant's date of death.
Fired-clay objects: Thermoluminescence (TL) dating is used to provide an estimate of the time since clay was fired to create the object.
Artifacts
Island Museum has acquired a collection of metal, fired clay, stone, bone, and wooden artifacts found on the Kaxna Islands, and presumed to be from the Kaxna Kingdom of 1250-850 BC. Researchers have mapped all the mines, quarries, and sources of clay on Kaxna and know that wooden artifacts of that time were generally created within 2 years after tree harvest. There is, however, considerable uncertainty as to whether these artifacts were actually created on Kaxna.
In analyzing these artifacts, the museum assumes that radiocarbon dating is accurate to approximately ±200 years and TL dating is accurate to approximately ±100 years.
Budget
For outside laboratory tests, the museum's first-year budget for the Kaxna collection allows unlimited IRMS testing, and a total of S7,000— equal to the cost of 4 TL tests plus 15 radiocarbon tests, or the cost of 40 ICP-MS tests—for all other tests. For each technique applied by an outside lab, the museum is charged a fixed price per artifact.
Among the Kaxna artifacts is a wooden box containing both a small fired-clay bead and some river sediment containing clay and plant matter. Based on the museum's assumptions, which one of the following details about the bead can be determined by applying one of the tests in the manner described?
A range of dates for its manufacture
The Kaxna island on which it was made
Vegetation patterns near the workshop where it was made
A range of dates for its placement in the box
The source of clay used to make the bead