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.
