It seems that overall population will continue to increase indefinitely given present trends, notwithstanding subzero growth among some populations. So that's one.
''Given current trends", that friend of mine who opened a shop 3 years ago and added a full-time employee in the spring (a doubling of the workforce every 2.5 years) will be requiring twelve billion workers just around the end of the century, so at least unemployment isn't going to be a problem.
Either that, or projecting current trends without looking at the underlying drivers is just a bad idea, in accordance with the motto "bullshit in, bullshit out". You pick.
What's worse, you're cherrypicking which trends you want to look at. One current trend is for the percentage population growth rate to decline - from 2.2 in the sixties to 1.15% today. If that's the trend you're projecting, we'll reach zero growth long before the end of the century. Another current trend is for the population to get older, and thus age-related deaths to increase massively in proportion to the population; an older population also means a smaller percentage of women in child-bearing age, so the birth rate is bound to decline
even if fertility rates stayed what they are. If you use the crude population growth rate (being as it is a composite of multiple drivers that must, and can, be directly assessed), you might as well project the freezing over of the Carribean by mid-November based on recent weather.
My second contention is that humans will exceed carrying capacity because humans are slowly degrading carrying capacity.
That is a potential concern. For most of the 20th and 21st century, however, this is not what we've observed. E. g. in the area of food production, yields per hectare have on the large been growing faster than the population.
My third contention is that general conditions over time are changing in the direction of less productive capacity IAC with entropy.
Are we talking in 100s, or 100s of millions of years here?
So, given all that humans will exceed carrying capacity and crash in the not too distant future.
Significantly less productive conditions due to entropy in the not too distant future? I want some of what you've been smoking!