The number of atoms of a radioactive substance at time t is given by

N(t) = N_oe^−t/τ ,

where N_o is the initial number of atoms and τ is the relaxation time. For ¹⁴C,τ = 8320y. Calculate the fraction of an initial sample of ¹⁴C that remains after 15.00 years, using Eq. (6.10). Calculate the correct fraction and compare it with your first answer.