Emergence XVII: Exponential Growth and Decay from Polarity and Acceleration

In the Emergence model, polarity π (sign of amplitude) and acceleration A (second derivative) are primitives. This paper shows that exponential growth and decay emerge when acceleration is proportional to amplitude. The sign of the product πA determines whether the function grows or decays. The base of the exponential (e, 2, 10, etc.) is a matter of convention, not a physical constant. The rate constant is proportional to πA. No new primitives are introduced. This paper is conceptual and speculative, intended for foundations of physics. It does not derive πA = e; rather, it shows that exponential behavior is possible within the primitives of the Emergence model. The analysis distinguishes unstable (exponential) from stable (oscillatory) cases and clarifies that the proportionality A ∝ Φ is a special case, not a universal derivation.