👉 Explosion math, also known as the Exponential Growth Model, describes a scenario where a quantity grows at an accelerating rate, leading to extremely rapid expansion over time. This is often modeled mathematically with the equation \( N(t) = N_0 e^{rt} \), where \( N(t) \) is the quantity at time \( t \), \( N_0 \) is the initial quantity, \( r \) is the growth rate, and \( e \) is the base of natural logarithms. The key characteristic is that the growth rate \( r \) itself increases exponentially with time, resulting in a steep curve that quickly surpasses any initial constraints. This model is commonly used to describe phenomena like population growth, compound interest, and the spread of diseases, where small initial changes can lead to massive outcomes over short periods.
