What is a exponential decay function?

An exponential decay function is a mathematical model that describes a process where a quantity decreases at a rate proportional to its current value. This type of function can be expressed in the form ( f(t) = a e^{-kt} ), where ( a ) is the initial amount, ( k ) is the decay constant, and ( t ) is time. As time progresses, the function approaches zero but never actually reaches it, illustrating how quantities like radioactive substances or population decline over time. Exponential decay is commonly observed in natural processes, such as the cooling of an object or the discharge of a capacitor.