In cell culture, when cells are inoculated into fresh media, there can be a period of slow (or lag phase) growth followed by a transition to exponential growth. This period of slow growth is usually attributed to the cells' adaptation to a new environment. However, we argue that, based on observations of shaken suspension culture of Dictyostelium discoideum, a model single-cell eukaryote, this transition is due to a density effect. Attempts to demonstrate the existence of implicit cell signaling via long-range diffusible messengers (i.e., soluble growth factors) through cell-medium separation and microfluidic flow perturbation experiments produced negative results. This, in turn, led to the development of a signaling model based on direct cell-to-cell contacts. Employing a scaling argument for the collision rate due to fluid shear, we reasonably estimate the crossover density for the transition into the exponential phase and fit the observed growth kinetics.