How do you represent an everlasting exponential (boldsymbol{e}^{-a t}) for (boldsymbol{t} geq mathbf{0}) and (boldsymbol{t}

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How do you represent an everlasting exponential \(\boldsymbol{e}^{-a t}\) for \(\boldsymbol{t} \geq \mathbf{0}\) and \(\boldsymbol{t}<\mathbf{0}\) ?

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