The half-life of 234U, uranium-234, is 2.52 105 yr. If 97.7% of the uranium in the original sample is present, what length of time (to the nearest thousand years) has elapsed?

Answer 1

.5 = e^2.52*10^5 k
ln .5 = 2.52 * 10^5 k
k =-2.75*10^-6

ln .977 = -2.75*10^-6 t
t = 8460 years
= 8,000 years

Answer 2

.977=1e^(.693t/thalf)

take lne of each side.
ln.977=.692t/th

t= thalf*ln.977/.693