text: 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).