2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164694We consider the Bernoulli first-passage percolation on $\mathbb Z^d (d\ge 2)$. That is, the edge passage time is taken independently to be 1 with probability $1-p$ and 0 otherwise. Let ${μ(p)}$ be the time constant. We prove in this paper that \[ μ(p_1)-μ({p_2})\ge \frac{μ(p_2)}{1-p_2}(p_2-p_1)\] for all $ 0\leq p_1<p_2< 1$ by using Russo's formula.7 pagesProbabilityMathematical Physics60K35; 82B43text