What does this even mean?
The exponential growth in food production would be a good thing.
Exponential growth in housing is a good thing. The exponential growth in alternative energy sources would also be a good thing.
These are all "physical systems" whose consistency we rely on. I don't believe your above statement is very well thought out. There seem to be many "physical systems" that grow exponentially, it's a necessity given the world's population grows exponentially.
No, exponential growth is almost universally bad except in a few systems where we can intentionally either check the growth or where the crash caused by the growth is the desired result.
An example of the former is a loaf of bread. Yeast grow exponentially. But if you leave a loaf too long, the yeast eats all the sugars, creates enough alcohol to kill the colony off, and you have a stinking slimy mess. But we know this, and at a certain point, before the Malthusian crash, we pop the loaf in a 350 degree oven, swiftly killing all the yeast while the load is in the desired state for baking.
An example of the latter is a nuclear detonation; It is a runaway exponential growth that is stopped only by the effects of its own operation, by exhaustion of fuel and disruption of the conditions required to burn it.
Lets take your example, exponential growth of food.
In fact, this is a classic Malthusian case.
Say we have an island on which there exist a population of foxes and a population of rabbits.
The conditions on the island are idea for rabbits, and they will reproduce, well, like bunnies.
If then ratio of foxes to rabbits is 0:1, that is, no foxes, the population of rabbits acts like our loaf of bread; Population expands until the island is stripped of anything that the rabbits can eat, and famine happens, and the population dies back severely to whatever population can get by on the tiny amount of food still growing, and the population levels do not recover until after the food sources do.
Any other ratio of foxes to rabbits, and the fox population grows along with the rabbit population but eventually, because rabbits leave the system through being eaten, but foxes accumulate, the foxes soon are eating rabbits faster than they can reproduce, the rabbit population crashes, and then the foxes are the ones to suffer the malthusian crash.
You can create a simple simulation and draw some very nice graphs to illustrate this and indeed you likely would have seen this in your high school biology text had you been paying attention.
Now, what if the food supply in the first case is artificially extended?
We add to the model a wildlife conservancy. They own Rabbit Island, and see that the rabbits are multiplying and that they will soon strip the island of food and have a crash. So they hire local lads with rowboats to bring bales of alfalfa to the island to feed the rabbits. Crisis averted? Nope.
What happens is that the population keeps growing, and the boys have to bring over more and more food for it, until they can no longer row fast enough to stay ahead of the growth curve, and the crash happens, but is MUCH WORSE than the natural crash we would have had if we had allowed the system to reach its own crisis. The island will have been utterly stripped of vegetation such that recovery at all would be in doubt, and the die-off may be so severe that extinction results.
This is the situation humanity is in. We were on track to have a world famine in the late 1970s; Human populations had not only outstripped arible land, but intensive use of the land was degrading it.
But then the Green Revolution happened; hybrids that were the result of increasingly-sophisticated genetic engineering techniques, pesticides, fertilizer, and mechanization meant that we had no Malthusian crisis, and that human population has continued to grow unchecked.
In this, we are now like the situation where the boys are adding food to the island system.
But the end is in sight; Crop yields have actually begun to decline in many parts of the world. Too-intensive agriculture depletes soil beyond the capacity of chemical fertilizers to deal with. Population pressure means that traditional crop rotation has been abandoned on much of the planet. Bugs are getting resistant to pesticides and weeds to herbicides. And we are running out of the oil required to feed the maws of the mechanical oxen we now use to farm on much of the planet.
The inevitable result, no matter what new technology is added to the system to forestall it, is the worst Malthusian crisis the planet has ever seen.
And at about the time it is happening, our CO2 greenhouse will be kicking in and will be making formerly arable lands useless, will be swamping fertile deltas and coastal areas, and displacing huge numbers of impoverished people.
If we get out of this without a MAJOR war over the last of the food, I will be astounded.