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Tetronian comments on Why are certain trends so precisely exponential? - Less Wrong
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I don't have an answer to your question, but I do have a concern: beware of positive bias. Don't just look for positive examples--how many trends are not precisely exponential? I'm pretty sure the answer is "a lot." (I know it sounds basic, but it bears repeating.)
In the last 5 years serial speed gains in computers fell off, while genomics took off. Both changes were quite abrupt.
More crucially, how many trends almost, but not quite look precisely exponential? Are precisely-exponential trends the tip of a long tail, or an additional local mode?
The logistic curve, for example, is extremely similar to the exponential curve for small values seeing as the latter is y' = ky and the former is y' = ky(1-y). That got Malthus with his whole doomsday arguments about population growth outstripping resources (at least for the time being).