Scaling laws describe how language model capabilities grow with compute and data, but say nothing about how long a model matters once released. We provide the first large-scale empirical account of how scientists adopt and abandon language models over time. We track 62 LLMs across over 108k citing papers (2018-2025), each with at least three years of post-release data, and classify every citation as active adoption or background reference to construct per-model adoption trajectories that raw citation counts cannot resolve. We find three regularities. First, scientific adoption follows an inverted-U trajectory: usage rises after release, peaks, and declines as newer models appear, a pattern we term the \textit{scientific adoption curve}. Second, this curve is compressing: each additional release year is associated with a 27\% reduction in time-to-peak adoption ($p < 0.001$), robust to minimum-age thresholds and controls for model size. Third, release timing dominates model-level attributes as a predictor of lifecycle dynamics. Release year explains both time-to-peak and scientific lifespan more strongly than architecture, openness, or scale, though model size and access modality retain modest predictive power for total adoption volume. Together, these findings complement scaling laws with adoption-side regularities and suggest that the forces driving rapid capability progress may be the same forces compressing scientific relevance.