This is demonstrably false. Let me demonstrably it for you:

Electricity is a renewable resource. Mankind has increased electricity exponentially.

Or another example, Dubai is a city that grew out of the sand within 15 years. Population exploded and with it the demand for clean water exploded. Your theory would state that it'd be impossible for Dubai to grow exponentially, because it would run out of water - water being produced only in a "linear" fashion.

But of course, Dubai doesn't care about your theory. The solution was simply to build more desalination plants, thus increasing clean water exponentially along with population.

Man creates the resources it needs. We make clean water. We grow trees. We find new energy when old sources run dry. If we can't do these things, prices rise and alternatives are found.

Your concerns about "deforestation" etc have to do with a lack of private property enforcement, and thus you see a tragedy of the commons. Protect private property and resource issues are null.