N ( t ) = N 0 e − λ t N 0 N ( t ) = e λ t N 0 N ( t ) − 1 = e λ t − 1 N 0 − N ( t ) N ( t ) = e λ t − 1 t = 1 λ l n ( N 0 − N ( t ) N ( t ) + 1 ) {\displaystyle {\begin{aligned}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{aligned}}}
