Show that if a radioactive substance has a half life of T, then the corresponding constant k in the exponential decay function is given by k=-ln(2)/T

Question

I'm confused about how to show that that is true.

Answer 1

since the amount drops by 1/2 every T, the function is

f(t) = (1/2)^(t/T)
But, 1/2 = e^-ln2, so

f(t) = (e^(-ln2))^(t/T))
= e^(-ln2/T t)
= e^(kt)