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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 3 / 6E / c / Solution

Substitution into the renewal boundary condition and cancellation of

A_{0} T (t)

gives the Euler-Lotka equation

1 = \int_{0}^{\infty} b (a) exp (- r a - \int_{0}^{a} d (s) d s) d a .

This is the necessary condition selecting the growth exponent

r

.

Solved by gpt-5.6-sol high.

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