We propose a simple theoretical dual economy model to study the dynamics of an economy in which individuals move out of a poverty trap. These dynamics are characterized by growth acceleration. This model implies that poverty reduction could, under some circumstances, cause growth, rather than the other way around. We define a measurement of the growth impulse that could be triggered by independent exits from poverty and correlate it with observed growth accelerations. This correlation is both positive and significant, and it passes various robustness checks.