I think it would be more accurate to say that human population growth rate has never been exponential and was never going to be, than to say that production has grown at a faster exponential rate.
Malthus has historically been excused with "just wait and see" explanations about his ideas, but no one seems able to say what is the kernel of truth in his theory or framework remains after you wipe away the details that were based on misunderstandings about his own time or about the actual dynamics of population growth.
For instance he paid almost no attention whatsoever to mortality rates or the disposition of ages within a population and their effect on growth rates. He also paid no attention to the relative fertility of families with different levels of wealth identified by Adam Smith long before him.
One way to summarize his work is that people's biological capacity to reproduce exceeds their physical capacity to increase the food supply, and that food supply is the ultimate constraint on human population that will be hit without other active constraints on population growth.
Of course humans have the ability to grow faster than their conditions support, or they would not be able to grow when conditions improved, or recover from traumas to a population. But they also have the capacity to not reproduce, and not replace people as quickly as they are dying. It seems like a real leap of faith, to claim that people can only be actively constrained in their fertility, since there hasn't been any evidence that people only limit family size when actively compelled to.
It is also strange to say that if there is no other limit on population growth, food will limit population growth. That's like arbitrarily stating that the only limit on fire is fuel, or that the only limit on fire is oxygen, or temperature. Population growth is a function with many inputs, and populations would approach some equilibrium even if food was hypothetically limitless.
Maybe the excuse is that food is just a metaphor for the basket of all resources that people need, and that it can still be argued that populations without active constraints on growth increase exponentially until they inevitably result in famine, plague or war to decrease their numbers.
What human populations work that way? They tend to ebb and flow in size around an equilibrium, then with a technological advance or environmental improvement they shift from one equilibrium to another at an increasing rate then a decreasing rate, just like a logistic function. Even with a collapse of a civilization the numbers decline like a logistic function. The curve might be steep, but it starts slowly, decreasing faster and faster then more slowly again as it gets close to zero.