At first yes, but not recently, now the opposite is true, if anything. We haven't had exponential growth since the 60s and are currently headed towards a steady state population because of improved standards of living. Turns out health and properity leads to smaller families.
We do still have significant growth, but that is largely because we're filling out the older demographics in many countries, the birth rate is largely under control already, and once the current generations spread through we'll be in a stead state (around 11 billion). In fact, there's no way to _stop_ this growth now, short of killing or sterilising people, since the birthrate is already under control, we're just waiting for the last exponential generations to get old.
see https://www.youtube.com/watch?v=2LyzBoHo5EI
Long term, we probably should encourage (slightly) sub-2 children per family to let the total population shrink, but that will take a long time (unless something disasterous happens)
https://www.science.org/content/article/experts-be-damned-wo...
...and as a result of that, the world's population has been growing and growing (and the standard of living of this population has also on average improved), which leads to more CO2 emissions, a higher consumption of finite natural resources etc. etc. Now there are two possible theories:
(1) things will continue to get better, if any problems will come up along the way we will surely be able to solve them.
(2) we are accelerating towards a brick wall which we can't see yet, but when we see it it will be too late to avoid the crash.