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!"
