I am stuck on a problem whereby, a drug has a half life of 36 hours, but every 24 hours 100g is added including at the start. So Q(0)=100g, I know how to do half life calculations but am struggling to fit it into a summation for any t!
Any help would be appreciated!
The overall drug weight $Q(t)$ after $N$ added doses (excluding the first one) will be: $$ Q(t)=Q(0)\left[\sum_{k=0}^{N} 2^{\frac{kT}\tau}\right] 2^{-\frac{t}\tau}, $$ where $T$ is the period of adding a dose (24 hours) and $\tau$ is the half life of the drug (36 hours). The function is discontinuous at points $t=kT $, $k\in\mathbb Z $.
One can get rid of $N$ in the equation using $N=\left\lfloor\frac tT\right\rfloor $, where $\left\lfloor x\right\rfloor $ is the floor function.