$$l=l_{0}(1+\alpha\Delta t)$$
$\left\{\begin{matrix}l_{0}=\frac{l}{t\Delta \alpha +1}\text{, }&t=0\text{ or }\Delta =0\text{ or }\alpha \neq -\frac{1}{t\Delta }\\l_{0}\in \mathrm{R}\text{, }&l=0\text{ and }\alpha =-\frac{1}{t\Delta }\text{ and }t\neq 0\text{ and }\Delta \neq 0\end{matrix}\right.$
$l=l_{0}\left(t\Delta \alpha +1\right)$