If the point is "name things that appeared to follow an ast…

If the point is "name things that appeared to follow an astonishingly clean curve until they didn't," economic history is littered with them.
Tulip bulb prices in the Dutch mania.
South Sea Company shares before the 1720 collapse.
Mississippi Company shares under John Law.
Japanese real estate prices in the 1980s.
Nasdaq technology stocks during the dot-com bubble.
U.S. housing prices before 2008.
Madoff's returns, which looked almost absurdly smooth and predictable.
Countless commodity super-cycles that appeared to exhibit stable long-term trends until demand changed.
More fundamentally, entire categories of growth processes exhibit log-linear behaviour over particular intervals:
Early railroad adoption.
Telephone penetration.
Internet adoption.
Mobile phone adoption.
Semiconductor cost and performance curves.
Storage density improvements.
The difference is that serious economists and statisticians do not look at a historical fit and conclude they have discovered a permanent law.
A curve fit describes data.
A theory explains data.
A predictive model survives out-of-sample testing.
The idiot's mistake is believing that because a chart has hugged a regression line for a while, the regression line caused the chart. That's roughly equivalent to observing that every rooster crow has been followed by sunrise and concluding that roosters control celestial mechanics.
The real question is not:
"How well does the historical data fit the curve?"
The real question is:
"What mechanism generates the curve, and why should it continue?"
That is usually where the conversation ends, because chart evangelists have a line on a graph but no underlying economic model.