Students will launch the investigation by testing first impressions against short real-world data cases, examining what strong modeling evidence looks like, and choosing an initial case for later study. They will generate early claims about exponential, logarithmic, linear, or logistic behavior, compare those claims with peers, and document a first-round question set and evidence plan for the modeling cycles ahead.

Students will investigate a short growth-or-decay data mystery, test early model ideas with exponential and logarithmic representations, refine a focused investigable question, and produce a peer-reviewed methodology plan that names what data, evidence, and comparison criteria they will use in the next phase.

Students will execute a traceable data-collection plan for their selected case, organize clean quantitative records, and conduct an early model-quality check by comparing linear and exponential behavior through tables, quick plots, residual snapshots, and revision notes. They will document methodological choices, test the reliability of their evidence, and revise their investigation approach before moving into full model construction.

Students will turn collected data into defensible exponential and logarithmic models, test those models with graphs and residuals, and document how evidence changes their equations, interpretations, and predictions in an annotated modeling portfolio.

Students will synthesize evidence from their modeling cycles, stress-test competing interpretations, and prepare polished public-facing artifacts that explain how their exponential, logarithmic, or logistic model was built, revised, and defended with data. They will use peer critique, prediction-check evidence, and clear mathematical communication to finalize an annotated portfolio section and an interactive exhibit station before the public expo.

Students will defend their final exponential, logarithmic, or logistic models in a public showcase, use audience evidence and prediction checks to evaluate model quality, and complete a concise final reflection that documents revisions, limitations, and next steps for mathematical investigation.