What is the defining characteristic of exponential decay?

Exponential decay is characterized primarily by a negative growth rate. This means that as time progresses, the quantity decreases at a rate proportional to its current value. In mathematical terms, exponential decay can typically be expressed in the form ( N(t) = N_0 e^{-kt} ), where ( N(t) ) represents the quantity at time ( t ), ( N_0 ) is the initial quantity, ( e ) is the base of the natural logarithm, ( k ) is a positive constant that indicates the decay rate, and ( t ) is time. Because ( k ) is positive, the exponent is negative, leading to a decay in value as time increases.

When examining the other choices, it becomes clear why they do not define exponential decay. Describing increasing values over time contradicts the very concept of decay, which inherently involves a decrease. A fixed base with a positive exponent applies more to exponential growth, where values increase rather than decrease. Finally, increasing asymptotically refers to a function that approaches a certain value but never actually reaches it, which is a feature of some types of growth but not decay. Thus, the defining characteristic of exponential decay is indeed the presence of a negative