A radioactive isotope has a half life of 25 years. There was 100 mg of the isotope in 2005.

Question

(a) Find an expression for the amount of the isotope, A(t), that is still active using time t, measured in years since 2005. Your expression must be of the form A(t)=Pe^ct (base "e").

Answer 1

You are modelling
amount = P e^(kt), where P is the original amount
so when t = 0 , P = 100
when t = 25, P = 50
50 = 100 e^(25k)
.5 = e^(25k)
ln .5= 25k
k = ln .5/25 = appr -0.027725... (I stored this in may calculator's memory)

amount = 100 e^(-.027725...(t))

Of course, if we had used a base of 1/2 it simply would have been
amount = 100 (1/2)^(t/25)

check: let t = 25 in both equations, both yield an amount of 50

Answer 2

Thank you!!