An unknown radioactive element decays into non-radioactive substances. In 580 days the radioactivity of a sample decreases by 47 percent. (a) What is the half-life of the element?

Answer 1

580 days decays 47% which leaves 53%

half life is when the decay is 50%> 47%

which should be a little longer than 580 days

.53 = e^580r

ln.53 = 580r

r = ln.53/580 =-.00109= .0109% decay rate daily

.5 = e^.00109t

ln.5 = .00109t

t = ln.5/.00109 = about 635.9 days days