What seems most likely is that something will eventually "put the brakes on" our growth. That something might be resource limitations, disease, accumulation of wastes or other limitations.
Let's think about it from perspective of what influences r. Birth and death rates influence r. It is probable that, as the population increased and resources became limiting, resource or other constraints (or wars over resources) would cause either d to increase or b to decrease, or both, diminishing r. The population growth rate would then slow, either gradually or cataclysmically, as in the case of major famines or pestilence.
Humans are unique among living things (as far as we know!) in that we can see what is happening to our population size, and we know that we have choices. If we want growth to slow, we can choose whether we will regulate our growth by regulating birth rates, or simply allow it to be regulated in "nature's way," by increasing death rates.
In a more idealized world, the trajectory of population growth would look more like the following:
You can see that the slope of the population growth rate curve gets steeper and steeper early on, and then begins to decrease as N increases, finally leveling off.
Growth following such a sigmoidal (or "s-shaped" curve) is called logistic growth.
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