An exponential decay can be described by any of the following four equivalent formulas:<big><math display="block">\begin{align}
  N(t) &= N_0 \left(\frac {1}{2}\right)^{\frac{t}{t_{1/2}}} \\
  N(t) &= N_0 2^{-\frac{t}{t_{1/2}}} \\
  N(t) &= N_0 e^{-\frac{t}{\tau}} \\
  N(t) &= N_0 e^{-\lambda t}
\end{align}
where
* is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),
* is the quantity that still remains and has not yet decayed after a time ,
* is the half-life of the decaying quantity,
* is a positive number called the mean lifetime of the decaying quantity,
* is a positive number called the decay constant of the decaying quantity.
The three parameters , , and  are directly related in the following way:where  is the natural logarithm of 2 (approximately 0.693).