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

Of the $a_t$ immature cells, a fraction $\lambda$ leaves by maturation and the rest remains immature. Of the $b_t$ mature cells, a fraction $\mu$ divides and is replaced by four immature cells, while a fraction $k$ dies; the remainder stays mature. These contributions give exactly