Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 4 / 6A / d / Solution

For $t\ge T$, set $\lambda =0$. Mature cells then decay geometrically:while their divisions add $4\mu b_{T+j}$ to the permanently immature population. If $\mu +k>0$, mature cells disappear andIf $\mu =k=0$, no further change occurs and the limit is $a_T+b_T$.