The real reason for the population explosion is the exploitation of easily obtainable energy sources. Specifically, coal, oil and natural gas. Exploiting these cheap sources of energy has allowed us to power machines which allow much greater food production, and better transportation options as well.
The real crisis will occur when those sources of energy become scarce.
Fortunately, we do have other sources of energy we can use. Unfortunately, those sources of energy cannot currently sustain even our current population, much less 10 billion of us. Ever seen what happens to bacteria in a petri dish? We're currently in the exponential phase of growth. After that will come the stationary phase (we're approaching that) and finally there's the death phase. Given the nature of humanity, there are likely to be few, if any, survivors. But that doesn't need to be the case.
The real question which should be answered is how many people can live on the planet sustainably? That's difficult to answer, but I believe it would be around 2 billion given current technologies. More than that if you're willing to make significant use of nuclear fission and much more than that if controlled nuclear fusion becomes a reality.
Curiosity is the single most important attribute with which humans are born. More than a simple desire to discover or know things, curiosity is a powerful tool, like a scalpel or a searchlight. Curiosity changes us. It is also a way to effect change, perhaps even on a global level.