Malthus noted that human population grew geometrically while food production increased arithmetically. He was writing during a time when steady population growth was emerging as a phenomenon. It should be noted that the graph doesn't differentiate between growth in different continents â€“ Malthus was describing population growth in Europe which, looking at the graph, may actually have been increasing geometrically at the time.
He also may have been describing potential
population growth. Let's assume that a European woman in Malthus's time had a reproductive window of twenty years. Maybe she had ten children and maybe a half dozen of them survived to reproductive age. If all the surviving children had families of their own with similar survival rates it's easy to see how population could increase at a rapid rate. In contrast, increased agricultural production could only be accomplished incrementally. New fields and pastures would have to be developed, technology might improve, new methods could be adopted â€” but none of those would happen at a rate matching the rate of population growth in the example.
If you are going to use the word, I am only asking that you provide a consistent definition.
I'm not using the word, other than to discuss its application.
If you can't distinguish between "exponential" growth, and any other kind of growth, than the word has no meaning.
A normal person would have little difficulty distinguishing its meaning by the context in which it is used. "Wow! The growth of manufactured housing in this trailer park has been exponential!"