User:Robert.McGibbon

$$\begin{align} N(t) = N_{0}e^{-\lambda t} \\ \frac{N_{0}}{N(t)} = e^{\lambda t}       \\ \frac{N_{0}}{N(t)} - 1 = e^{\lambda t} - 1\\ \frac{N_{0} - N(t)}{N(t)} = e^{\lambda t} - 1\\ t = \frac{1}{\lambda} ln(\frac{N_{0}-N(t)}{N(t)} + 1)\\ \end{align} $$