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For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value.
Quantities subject to exponential decay are commonly denoted by the symbol N. (This convention suggests a decaying number of discrete items. This interpretation is valid in many, but not all, cases of exponential decay.) If the quantity is denoted by the symbol N, the value of N at a time t is given by the formula:
where
When t=0, the exponential is equal to 1, and N(t) is equal to . As t approaches infinity, the exponential approaches zero.
In particular, there is a time such that:
Substituting into the formula above, we have: