Question

The age of fossils can sometimes be determined by radiometric dating, which is based on the constant rate of decay of radioactive isotopes. the time required for half of a radioactive isotope to decay is called the half-life of that isotope. for example, the isotope carbon-14 has a half-life of 5,730 years. suppose it is determined that a fossilized leaf contains 12.5% of the carbon-14 that was present when the fossil formed. how old is the fossil? express your answer numerically.

Answer 1

The age of the fossil given the present amount of Carbon-14 is given in the equation,
                               A(t) = A(o)(0.5)^t/h
where A(t) is the current amount, A(o) is the initial amount, t is time and h is the half-life. Substituting the known values to the equation,
                       A(t) / A(o) = 0.125 = (0.5)^(t/5730)
The value of t from the equation is 17190.
Thus, the age of the fossil is mostly likely to be 17190 years old.