  In this paper we observe the frog model, an infinite system of interacting
random walks, on Z with an asymmetric underlying random walk. Under the
assumption of transience with a fixed frog distribution, we construct an
explicit formula for the moments of the lower bound of the model's long-run
range, as well as their asymptotic limits as the drift of the underlying random
walk vanishes. We also provide conditions in which the lower bound can be
scaled to converge in probability to the degenerate distribution at 1 as the
drift vanishes.
