Exponential Models

Fold a piece of paper in half, and it's 2 sheets thick. Fold again: 4. Again: 8. By fold 42, the stack would reach the Moon. That's the terror and beauty of exponential growth — it doesn't add a constant amount each step, it MULTIPLIES by a constant ratio. The result is a curve that starts gently and then vaults past every linear prediction. The same logic, run in reverse, governs radioactive decay: half the atoms vanish every half-life, forever shrinking by a fixed fraction.