I don't think that's entirely clear. There's a concept in economics called dematerialization. From wikipedia: Dematerialization refers to the absolute or relative reduction in the quantity of materials required to serve economic functions in society.
The idea is that as a country becomes more developed and prosperous, the less resources are required to serve the needs of the people. For instance: Between 1977 and 2001, the amount of material required to meet all needs of Americans fell from 1.18 trillion pounds to 1.08 trillion pounds. The incredible thing is that this seems to be a reduction in absolute resources not resources per populace. Much of that reduction is due to technology (e.g. a cell phone replaced plastic from camcorder, camera, computer etc). The other is due to production efficiencies and migration to cities . A similar trend can be seen with carbon reduction in developed parts of the world.
I'm not 100% convinced by this idea, but it's enough for me to question the premise that economic growth leads to more resource consumption.
https://en.wikipedia.org/wiki/Dematerialization_(economics)
[Edit] There's a great interview with Andrew McAfee on this concept at EconTalk. Its based on the McAffe's book More from Less that explores the topics. He mentions a few limitations of the idea including environmental concerns