Activity, age and series in code

You will write three functions about activity, dating and decay series.

The idea. The activity falls as $R = R_0\,2^{-t/T}$. The age of a sample is $t = T\log_2\dfrac{R_0}{R}$. In a series an alpha decay changes $(A, Z)$ by $(-4, -2)$ and a beta-minus decay changes it by $(0, +1)$.

Your tasks.

1. In activity_after, return the activity after a time t, for the starting activity r0.
2. In age_from_fraction, return the age in the unit of half_life, for the fraction fraction of the activity that is left.
3. In after_decays, return the pair (a, z) after alphas alpha decays and betas beta-minus decays.