👉 The concept of exponential growth and decay is a fundamental comparison in mathematics, seen across various fields like physics, biology, and economics. In exponential growth, quantities increase at a rate proportional to their current value, often modeled by the equation \( P(t) = P_0 e^{rt} \), where \( P_0 \) is the initial quantity, \( r \) is the growth rate, and \( t \) is time. Conversely, exponential decay follows a similar pattern but with a negative growth rate, represented by \( P(t) = P_0 e^{-rt} \). Both processes illustrate how small initial changes can lead to significant outcomes over time, governed by the same underlying mathematical principles but applied differently in contexts such as population growth versus radioactive decay.
