= Solution
The second analysis is an exposure-adjusted <Poisson regression> for case counts:
$$
\boxed{C_{gj}\sim\operatorname{Poisson}(\lambda_{gj}),\qquad\log\lambda_{gj}=\log N_{gj}+\alpha_P+a_{P,j}+\gamma_Pg,\qquad a_{P,15\text{–}24}=0.}
$$
Cell counts are independent, and their conditional <variance> equals their conditional mean. The population term is an <offset> with coefficient fixed at one. Thus the fitted case rate is $\lambda_{gj}/N_{gj}=\exp(\alpha_P+a_{P,j}+\gamma_Pg)$; treating $\log N_{gj}$ as a free <covariate> would fit a different model. Age multipliers and the adjusted city rate ratio are exponentials of the corresponding <regression coefficients>.
The fitted model again has nine parameters and six residual <degrees of freedom>. Sequential additions of age and city reduce the <Poisson deviance> by $2095.56$ on seven <degrees of freedom> and $226.52$ on one, respectively. The residual <deviance> is $5.21$, close to the six residual <degrees of freedom>. The city <likelihood-ratio test> is overwhelmingly significant, as in the binomial analysis. The table provides no Poisson coefficient estimates, so an exact Poisson city rate ratio cannot be read from it.
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