Decay rate,k is 8.1% per year=-0.081. What is the half-life in years

Question

Need some assistance, any help is greatly appreciated. Thanks!

Answer 1

N/N₀ = e^-kt = (1/2)^{t/t(1/2 life)} = 2^{-t/t(1/2 life)}

You solve this for k by taking the ln of both sides:

-kt = ln(2^t/t(1/2life)) =- (t/t_1/2)ln(2)

k = ln(2)/t_1/2

which can easily be solved for half-life in terms of k.

Take care.