Question
A radioactive substance decays exponentially in such a way that after 50 years, 60% of the initial amount remains. Find an expression for the quantity remaining after t years.
Answers
Reiny
R(t) = e^kt, where R(t) is the percentage remaining after t t years, k is a constant
given: when t = 50 , R(50) = .6
.6 = e^(50k)
ln both sides
ln.6 = 50k lne
k = ln.6/50
R(t) = e^( (ln.6/50) t)
given: when t = 50 , R(50) = .6
.6 = e^(50k)
ln both sides
ln.6 = 50k lne
k = ln.6/50
R(t) = e^( (ln.6/50) t)