Derive relationship between radioactive constant and half life

[quantic123]

Hi,

I was wondering how to derive relationship between radiocative constant and half life, which is t_1/2=ln2/b, where b=decay constant.

It seemed like the it was just replaced into the equation A=A₀(1/2)^t/t_1/2.

Thanks in advance

 

[mfb]

From $A=A_0 e^{-bt}$, just manipulate the exponential: $$A=A_0 e^{-bt}=A_0 2^{\frac{-bt}{\ln(2)}} = A_0 2^{-\frac{t}{t_{1/2}}}$$