Why Biology Thinks in Exponentials
Why Biology Thinks in Exponentials Why Biology Thinks in Exponentials Beautiful question — and this time the answer is not symbolic at all. In biology, the number $e$ appears because living systems change continuously, and $e$ is the mathematics of continuous change. Below, we explore the main biological domains where exponentials naturally emerge — with intuition first, equations second. 1️⃣ Population Growth (The Classical Case) Intuition Reproduction is proportional to population size Resources are not yet limiting Time is continuous Model $$\frac{dN}{dt} = rN$$ Solution $$N(t) = N_0 e^{rt}$$ Where it appears Bacterial cultures (early phase) Cell division Tumor growth (initial stages) Microbial ecology 🧠 More individuals → more births → faster growth. 2️⃣ Enzyme Kinetics & Biochemical Reactions Many biological reactions depend on rates proportional to...