In all this talk about logistic population growth and carrying capacities, it's important to recognize that the human population, in a worldwide sense, also has a carrying capacity. The Earth cannot sustain an infinite number of humans any more than it can sustain an infinite number of emperor penguins. This we know for certain. The difficult question to answer, however, is what the exact, or even estimated, worldwide carrying capacity for humans is. The reason that human carrying capacity is hard to know exactly is the same as the reason for other populations.
Carrying capacities are not stable or constant because they are functions of resources. If resources increase, if species find new ways to utilize their existing resources, or if species find entirely new resources, the carrying capacity for that species will likewise increase. Most species are fairly limited in how they increase their own carrying capacity. Humans, on the other hand, are exceedingly adept at it. We find ways to increase the number and types of places we can live. We find innovative ways to utilize ever-decreasing natural resources. We even find entirely new natural resources, like wind power and solar energy. We find exciting, and often controversial, ways to increase food production and quality. We find ways to decrease death rates at higher and higher population densities. In short, we are really good at increasing our carrying capacity. However, most biologists believe that we cannot do so forever. Eventually, we will reach the Earth's sustainable limit for our species.
Currently, the human population has an average growth rate of 0.012. This may seem like a small number, but when you multiply 0.012 by the current population size (nearly 7 billion), the result is about 84 million! That number means that the human population is growing by over 80 million people per year. And, because we haven't reached our carrying capacity yet, we are still in an exponential-like growth phase. At the current rate of 0.012, by the year 2050 (that's well within your lifetime), the human population will have over 11 billion individuals. By 2100, the 20 billion mark will have been surpassed by nearly 500 million. Those are enormous numbers.
Can the earth handle such a large population of an extremely high-resource consuming species? Doubtful. While estimates vary widely, most biologists predict the human carrying capacity to be around 11 billion. In the not too distant past, 11 billion people seemed like an impossibility. Today, it is a near-certainty. Even if every couple on earth from this point forward only had two children, the human population would continue to grow for another 40 years, causing the human population to top 11 billion. This residual 40-year growth would occur because there are so many young people in the population who still haven't entered the reproductive age group.3
So, what's to be done? The question is an ethical one to be sure. Some heavily populated countries, like China, have implemented reproductive caps, allowing only one or two children per couple (with little success). Some people, both inside and outside China, see this as a necessary evil. But, many people in the world view such a regulation as overly restrictive of individual freedom. Such contrasting viewpoints highlight the ethical dilemma posed by rapid human population growth. Aside from decreasing birth rates, what other solutions are there?
Since efforts to decrease birth rates at a global level are likely doomed to failure, and efforts to increase death rates are inhumane, it seems the only other "solution" is to increase the human carrying capacity. We humans are good at this, so we expect there will be some success in such efforts. However, any successes will be short-lived as there is most certainly an absolute limit to the number of humans the Earth can support (even if this number is well over 11 billion).
What's more, the ethics of increasing human carrying capacity should be considered as well. At what, or whose, expense should it be undertaken? As the human population increases, other species are and will be negatively affected. Human expansion into new habitats decreases habitat space for other organisms. The same thing happens as we increase and expand our agricultural activities. Lastly, climate change attributable to human activities is having severe impacts on species all over the planet. As the human population increases, the consequences of human activities will also be amplified. For this and the other reasons touched on above, human population growth may be the ethical quagmire of the century.