What is the definition of exponential decay?

Exponential decay refers to a process where a quantity decreases at a rate proportional to its current value, resulting in a rapid decline over time. Mathematically, it can be represented by the equation (N(t) = N_0 e^{-kt}), where (N(t)) is the quantity at time (t), (N_0) is the initial quantity, (k) is the decay constant, and (e) is the base of the natural logarithm. This phenomenon is commonly observed in various natural processes, such as radioactive decay and the cooling of hot objects.