This paper focuses on growth feasibility in an era of increasing scarcity of fossil fuels. A stylised dynamic model illustrates the implications of investing in smooth technological progress in the field of renewable energy. Positive rates of GDP growth sustained by fossil fuels entail, on the one hand, more income available for R&D in renewable energy sources, and on the other, an acceleration of the exhaustible resource depletion time. Our model explores such a trade-off and highlights the danger of high growth rates. Policies should target low growth rates, stimulate investment in alternative energy sources and discourage consumption growth.