= Solution
Write $r=1,\ldots,16$ for rats and $j$ for repeated observations. With diet 1 as the <reference level in a regression factor>, the <random-intercept linear mixed model> is
$$
Y_{rj}=\beta_0+\beta_Tt_{rj}+\beta_2\mathbf1_{\{D_r=2\}}+\beta_3\mathbf1_{\{D_r=3\}}+b_r+\varepsilon_{rj},
\qquad b_r\overset{\mathrm{iid}}\sim N(0,\tau^2),\quad\varepsilon_{rj}\overset{\mathrm{iid}}\sim N(0,\sigma^2),
$$
with the two families of <normal distributions> independent and the covariates treated as fixed. The reported estimates are
$$
\boxed{(\widehat\beta_0,\widehat\beta_T,\widehat\beta_2,\widehat\beta_3)=(244.06890,\,0.58568,\,220.98864,\,262.07955),\quad\widehat\tau^2=1337.88,\quad\widehat\sigma^2=66.85.}
$$
The corresponding estimated standard deviations are $36.577$ and $8.176$ grams. Individual realized <random intercepts> are not parameters in this marginal model, and their predictions are not supplied by this summary. For distinct measurements on the same rat, $\operatorname{Cov}(Y_{rj},Y_{rk})=\tau^2$, while the marginal <variance> is $\tau^2+\sigma^2$; different rats are independent.
The estimated mean weight rises by $0.58568$ grams per day, adjusting for diet and the rat's <random intercept>. This common slope is imposed across all diets: there is no time-by-diet <interaction term>, so these estimates do not compare diet-specific growth slopes. The intercept refers to time zero for diet 1 and a zero rat effect.
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