We conduct a unique, Amazon MTurk-based global experiment to investigate the importance of an exponential-growth prediction bias (EGPB) in understanding why the COVID-19 outbreak has exploded. The scientific basis for our inquiry is the well-established fact that disease spread, especially in the initial stages, follows an exponential function meaning few positive cases can explode into a widespread pandemic if the disease is sufficiently transmittable. We define prediction bias as the systematic error arising from faulty prediction of the number of cases x-weeks hence when presented with y-weeks of prior, actual data on the same. Our design permits us to identify the root of this under-prediction as an EGPB arising from the general tendency to underestimate the speed at which exponential processes unfold. Our data reveals that the "degree of convexity" reflected in the predicted path of the disease is significantly and substantially lower than the actual path. The bias is significantly higher for respondents from countries at a later stage relative to those at an early stage of disease progression. We find that individuals who exhibit EGPB are also more likely to reveal markedly reduced compliance with the WHO-recommended safety measures, find general violations of safety protocols less alarming, and show greater faith in their government's actions. A simple behavioral nudge which shows prior data in terms of raw numbers, as opposed to a graph, causally reduces EGPB. Clear communication of risk via raw numbers could increase accuracy of risk perception, in turn facilitating compliance with suggested protective behaviors.