Do men who extrapolate ever have erections?
I have to wonder. It must be terrifying - if the rate of growth were sustained long enough, Paul Ehrlich's phallus would exceed the volume of the known universe. And when it receded! - it could continue to grow smaller and smaller, perhaps forming a black hole and sucking in the entire planet.
If there's a Stupid Example Hall of Fame, the above could be a finalist. But really, some phenomena are self-limiting, and others come and go with changing conditions. And we can't say that we know what's happening beyond those most extreme data points we have available.
Take boiling, for instance. You might think that the hotter the fire you have under the pan, the faster the water in it will boil. That's true over a range, but then at a certain point the higher temperatures actually make things worse. This phenomenon must be taken into account when designing nuclear reactors, among other things. (Test it yourself with a hot frying pan - flick drops of water on it as you heat it. As the temperature rises, the drops will spread out and evaporate instantly. But at some point before you ruin your pan, the drops will form a ball and skate around the surface.)
Then there's freezing. Liquid water gets more dense the colder it gets, until just a few degrees above freezing. Then it starts to expand, so much so that by the time it freezes the ice has a lower density than the liquid around it. Which is why ice floats.
There are plenty more examples. Compressible fluids behave differently as their velocities approach the speed of sound. It's well known in medicine that "the dose makes the poison", and you can die from drinking too much water. Extrapolate biological responses to radiation doses down from Hiroshima levels to zero and the resulting predictions turn out way high. Tax receipts can actually decrease as you increase tax rates. And calculations involving subatomic particles must take quantum-mechanical and relativistic phenomena into account - simple Newtonian mechanics don't work anymore.
So we have to be careful when we extrapolate. We're familiar with the phenomena that I described above, but I dare say that we haven't seen everything yet. Especially under the extreme conditions that are found in stars or other remote parts of the universe.
Yet it is popular to presume that the laws of physics can be extrapolated all the way to their singularities or beyond. Having done so, some claim that the universe resulted from a "big bang". Who knows, maybe it's true. But the fact is, we haven't seen a big bang. So we can't know if our extrapolations have led to situations like the above, when the rules change.
Hmm. Why would scientists persist in formulating such predictions, even pushing them to be taught in our schools? Ask Bryan Preston.