In this paper we derive optimal growth estimates on the potential functions of complete noncompact shrinking solitons. Based
on this, we prove that a complete noncompact gradient shrinking Ricci soliton has at most Euclidean volume growth. This latter
result can be viewed as an analog of the well-known volume comparison theorem of Bishop that a complete noncompact Riemannian
manifold with nonnegative Ricci curvature has at most Euclidean volume growth.