Asked by Doug
If 80 percent of radioactive element is left after 250 years, then what percent remains after 600 years? What is the half life of the element?
Answers
Answered by
Reiny
Assuming exponential decay
amount = a e^(kt) where a is the initial amount, and t is number of years
.8 = 1 e^(250k(
ln .8 = ln e^(250k)
ln .8 = 250k
k = ln.8/250
after 600 years ?
amount = 1 e^(600ln.8/250) = .5853 or appr 58.5%
for half-life ?
.5 = e^(ln.8 t/250)
ln.5 = ln.8/250 t
t = 250ln .5/ln .8 = 776.6 years
amount = a e^(kt) where a is the initial amount, and t is number of years
.8 = 1 e^(250k(
ln .8 = ln e^(250k)
ln .8 = 250k
k = ln.8/250
after 600 years ?
amount = 1 e^(600ln.8/250) = .5853 or appr 58.5%
for half-life ?
.5 = e^(ln.8 t/250)
ln.5 = ln.8/250 t
t = 250ln .5/ln .8 = 776.6 years
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