Final answer:
The age of the sheepskin parchment can be determined by calculating the time it has decayed based on the percentage of carbon-14 remaining, which is 40% of the atmospheric level, and the known half-life of carbon-14, which is 5,730 years.
Step-by-step explanation:
The question asks us to determine the age of a sample of sheepskin parchment using radiocarbon dating, based on the C14-to-C12 ratio present in the sample. Carbon-14 (C14) dating involves measuring the amount of carbon-14 remaining in an artifact compared to the amount in the atmosphere to ascertain its age.
Living organisms maintain a constant ratio of carbon isotopes, including carbon-12 (C12) and carbon-14, but when they die, they no longer absorb carbon, and the carbon-14 begins to decay at a known rate, with a half-life of 5,730 years.
In this case, the parchment has a C14-to-C12 ratio that is 40% of what is found in the atmosphere. To find the age of the parchment, we would use the formula N = N0 * e^(-lambda*t), where 'N' is the current amount of carbon-14, 'N0' is the original amount of carbon-14, 'lambda' is the decay constant, and 't' is the time in years since the parchment was made. The decay constant 'lambda' can be found using the half-life equation lambda = ln(2) / half-life (the half-life of C14 being 5,730 years).
By arranging and solving the formula for 't', we can then determine the age of the parchment. Due to the complex nature of these calculations and the need for logarithmic functions, usually, a graph or calculator capable of handling exponential equations is used to find the exact age.