One of my pet peeves is the misuse of exponential growth. I saw that moniker used to describe linear growth in a "Every worker produces more."-setting. I saw it, more understandably, used to describe quadratic or cubic growth, where increasing in two or three components causes an associated growth in output. For example and simulanteous increase in worker number and worker productivity gives a quadratic effect in overall output. But all of those are not exponential growth.
To even reach exponential growth is quite rare to be honest. Live - self-reproducing entities - are the only system I know to actually reach exponential growth. Where every entity is capable of not just reproducing itself, but of producing some more entities capable of reproducing themselves.
There are only two other system, where exponential growth is assumed to occur. One of those is the economy and the other one technology. The economy view on this lead me to formulate the important take-away that is the title:
There is not unlimited exponential growth.
That they often calculate in exponentials and percentage in economy is probably a quite damaging concept and may be due to a confusion of the time-declining value of money with the comparatively constant value of things actively used in economic exchange. In short a confusion of inflation - which is an exponential decrease - and productivity gains - which are most likely low order polynomials.
With respect to technology I am not sure. I know that Moore's Law worked for many years with respect to calculation speeds and is still working with regard to transistor density and memory growth. But I believe the end of the exponential growth in clock speed - calculations per second - is very fundamental to the overall process.
We are currently still using the after-effect of that growth to do great things in science and technology, but overall the end of the exponential growth is in sight and the technological singularity has been cancelled.
Well to be honest: For the singularity to work one needs not just a continuation of exponential growth - there is no unlimited exponential growth - but actually an exponential acceleration of the exponential growth. This is a very, very wild assumption. If that is possible whatever would then appear should have covered the universe already.
My guess how the idea of the singularity appeared is the following: If one has a population above the half of its carrying capacity, the growth rate increases if one lifts the carrying capacity - e.g. through technological advances or access to new resources. This can give the impression of an increase in the growth rate.
But the fundamental growth rate of the population - the time it takes for an individuum of the population to recreate itself - stays the same. Modern population dynamics rather point in the other direction - that the time to procreate increases for humans and especially for humans capable of advancing the technological barriers. Or soon for general entities capable to advancing technological barriers.