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Radioactive decay is a process where unstable atomic nuclei lose energy by emitting radiation in the form of particles or electromagnetic waves. The rate of decay of a radioactive substance depends on the number of radioactive atoms present at any given time. The rate of decay is proportional to the quantity of radioactive atoms, which can be described by the equation: N(t) = N_0 e^{-\lambda t} where N(t) represents the number of radioactive atoms at time t, N_0 is the initial number of radioactive atoms, e is the base of the natural logarithm, \lambda is the decay constant (which is characteristic of the radioactive substance), and t is the time elapsed.

Another example of a process that experiences exponential decay is the cooling of an object. According to Newton's law of cooling, the rate at which an object cools is proportional to the difference in temperature between the object and its surroundings. This can be modeled by an exponential decay function, as the temperature of the object approaches that of the surroundings. The equation that describes this process is: T(t) = T_s + (T_0 - T_s) e^{-kt} where T(t) is the temperature of the object at time t, T_s is the constant temperature of the surroundings, T_0 is the initial temperature of the object, k is the cooling constant (which depends on the object's properties and the surrounding environment), and t is the time elapsed.