The activity of the daughter is given by the Bateman equation:
where  and  are the activity of the parent and daughter, respectively.  and  are the half-lives (inverses of reaction rates  in the above equation modulo ln(2)) of the parent and daughter, respectively, and BR is the branching ratio.
In transient equilibrium, the Bateman equation cannot be simplified by assuming the daughters half-life is negligible compared to the parents half-life. The ratio of daughter-to-parent activity is given by: