It is an error, regardless of what you mean by "current trends continue" (you have defended a couple of mutually exclusive possibilities - that the population is plateauing, that the second derivative is on average constant, etc. I'll let you choose). For example, if you mean that the second derivative remains at or near its current negative value - as a constant, or average constant, or variation around the current mean, or whatever - your conclusion of a plateau is false. Your model would produce a crash - the doomsayer's vision. You are confused about something in an undergraduate calculus course. A horizontal line, a plateau in a population graph, has a second derivative of zero - approached from above or below. Or consider the example I posted above - the square root function. That could model the effect of a braking force of some kind, right? Graph it, and look at the second derivative. Compare. Takehome: the possibility of a bust of the current boom cannot be dismissed, or even cast into doubt, by pointing to a negative second derivative in the growth function. The question of overshoot and permanent loss of carrying capacity - like rabbits on an island, or the fate of the Easter Island settlers, both of which undoubtedly exhibited negative second derivatives in their population growth functions as they approached the mass dieoff - is not answered by pointing to negative second derivatives.