A specimen of charcoal found at Stonehenge contains 63% as much Carbon-14 as a sample of present-day charcoal. What is the age of the sample?

Since we are given with the identity of the chemical as Carbon-14, we obtain the half-life of the chemical from a reliable source and get a value of 5730 years. The equation that we are going to use for this item is,

A (t) / A (0) = (0.50) ^ (n/5730)

where A (t) is the current amount, A (0) is the initial amount and n is the number of years. We know from the given that the ratio of A (t) and A (0) is equal to 0.63. Substituting this to the given,

0.63 = 0.50^ (n/5730)

n = 3819.48

Thus, the sample is approximately 3819.5 years old.