World population growth is not exponential, but logistic. A logistic curve looks exponential until you pass the inflection point. IIRC, we did that in the '80s.

Yes[1]; most of the current population estimates show the world population leveling off in the 9-12 billion range. Percentage growth rate actually peaked in the mid 1960s (about 2.2%), and absolute growth peaked in the late 1980s (about 85 million people per year.) This is completely expected from logistic growth models[2].

Different species reach logistic growth in different ways. As the grandparent post noted, "reduced birth rate" is better than alternatives like "mass starvation". Lower birth rates are not a bad thing from a population growth perspective, though the demographic shift they bring about will require changes to our expectations regarding retirement. It's rather unfortunate that we're still using a retirement model designed when life expectancy was lower and birth rates were higher.

[1]"Who's that insightful person who posted about logistic growth and stole my thunder? Oh, hi, honey!"

[2]The image at http://www.growth-dynamics.com/articles/Kurzweil_files/image... shows actual world population data following a logistic curve, compared to an exponential curve above.

Fortunately, another limit is imposed by women getting access to education and then birth control. That has played a huge part in bringing the birth rate down.