To make progress toward a comprehensive theory of sustainable growth, this paper integrates fertility choice and exhaustible resource dynamics in a tractable model of endogenous technological change. The model identifies conditions under which the interdependence of population, resources and technology produces a transition that consists of three phases: (1) an initial phase where agents exploit exhaustible natural resources to support population growth; (2) an intermediate phase where agents turn on the Schumpeterian engine of endogenous innovation in response to population-led market expansion; (3) a terminal phase where knowledge accumulation becomes the sole engine of growth. The last phase is crucial: not only economic growth no longer requires growth of physical inputs, but technological change also compensates for the exhaustion of the natural resource.