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Patent Granted A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant: \frac{dN}{dt} = -\lambda N. The solution to this equation (see derivation below) is: N(t) = N_0 e^{-\lambda t}. \,