If it’s not an exponential curve, then what is it? Perhaps part of the cognitive problem here is that population growth is often quoted as a percentage of the current total (see https://en.wikipedia.org/wiki/Population_growth) which is inherently exponential. But the description is then that the exponential growth rate is dropping. This is what you would get if the growth rate was actually linear. Which is what you would see if the time to add a billion people is pretty much constant from 1960 to now and predicted to stay constant till 2025 at least. And that’s what’s quoted at that link with each extra billion taking 12-14 years. That may not be exponential, but it’s still a huge rate of growth and it’s not slowing down. Currently that 12-14 years to add a billion people is not extending. There are arguments that improved education, resulting drops in the birth rate and so on will result in fewer additional people each year and that it might even go negative but it’s not happening yet.
The more extreme predictions of people like Bartlett and Erlich that total population will keep accelerating because the exponential growth is constant may be inaccurate and exaggerated, but that doesn’t mean that population growth has gone away and the results of that aren’t a problem. Both now and in the short term future (<75 years, 1 lifetime). Even Joel Cohen in the papers described in TFA recognises this. So I don’t really see how linear instead of exponential growth is a justification for much optimism.