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In this paper, we prove the exact orders of critical intensity $u_*(T)$ inFinitary Random Interlacements (FRI) in $\mathbb{Z}^d, \ d\ge 3$ with respectto the expected fiber length $T$. We show that as $T\to\infty$,  $u_*(T)\sim T^{-1}, \ d\ge 5;$  $u_*(T)\sim T^{-1}\log T, \ d=4;$  $u_*(T)\sim T^{-1/2},\ d=3.$  Our estimates also give the order of magnitude at which the percolative phasetransition with respect to $T$ takes place.

On the exact orders of critical value in Finitary Random Interlacements