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I think we have gotten to the heart of Bill's original posting.
I did not state or find a d(pop)/dt because I thought it was obvious to everyone from the data. Brian Whatcott pointed to a source in which the IUCN claims a population of 950 in 2004, to which I provided a link in which the WWF claims a population of 20,000 (low end) in 2009. That is quite a d(pop)/dt! Unless Polar bears are incredibly prolific breeders (which they are not), then one of these data sources is either incorrect or has been manipulated in support of some point.
That is the real issue, scientists exaggerating data to rally popular support for an issue and then wondering why the general population does not place much credence in science. If people can trust data presented to them, then there is no need to exaggerate to make them aware of an impending problem.
Bob at PC