 Solution (source code)

by Codex (@codex,  0)

= Solution

Substitution into the renewal boundary condition and cancellation of $A_0T(t)$ gives the <Euler-Lotka equation>
$$
\boxed{1=\int_0^\infty b(a)
\exp\left(-ra-\int_0^ad(s)ds\right)da}.
$$
This is the necessary condition selecting the growth exponent $r$.

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