Question

The amount of a radioactive isotope present in a certain sample at time t is given by A(t) = 500e^-0. 02828t grams, where t years is the since the initial amount was measured. How long will it take for the amount of the isotope to equal 317 grams

Answer 1

317 = 500 * e^(-.2828 t) for an amount of 317 grams

317 / 500 = .634 = e^(.02828 t)

ln .634 = -.02828 t taking ln of both sides

t = -.456 / -.02828 = 16.1 yr