We do not know if resources are finite.
We know that the resources we have now are finite. But we don't know that in the future because we don't know what the technological set available to mankind will be.
Your argument assumes
1. We continue to consume those resources at a similar rate, and
2. Only those resources will be used in the future.
Perhaps in 75 years, we'll have cars that get 5,000 miles to the gallon.
Advents in nanotechnology may decrease the demand for copper by 90% as the atomic structure of copper products is strengthened.
Perhaps all power will be harnassed by wind or solar in a century.
That's all wild speculation, but we don't know. We have no idea. Did you know what the Internet was 15 years ago?
If a static population meets with a severe shortage of resources in a short period of time, i.e. famine in Ethiopia, then obviously, population will decline. But otherwise, the only finite limitation is the bounds of technological innovation.