= Solution
Apply the same vertical-then-horizontal cobweb construction to $H(u)=9ue^{-u}$. Since no numerical value of the large initial <biological population> is prescribed, an exact five-generation list is $u_1$, $H(u_1)$, $H^2(u_1)$, $H^3(u_1)$, $H^4(u_1)$. For the plotted example $u_1=5$, these values are
$$
\boxed{5,\quad0.303208,\quad2.015121,\quad2.417618,\quad1.939421.}
$$
The initial slump is followed by rapid growth and an alternating overshoot about $\log9\simeq2.197225$, which is now unstable because its <periodic-orbit multiplier> $1-\log9<-1$. A still larger initial <biological population> can remain extremely small for more than these four updates; the example illustrates the requested construction without imposing an unstated universal numerical starting value.
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