[Curious Cat (OP)]

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[Bored chemist]

Really?
When was the last time U saw quadratic/al/ly? I can't remember.
All I can remember is nonlinear and exponential/ly.

Well, there's a stack of references to the inverse square law.
Most functions aren't quadratic.
Plenty of things - notably economic and microbiological growth are roughly exponential.
So, you see exponential used a lot, because it's often the right word (and often "figuratively" the right word).

[alancalverd]

Journalists and politicians now use exponential to mean rapid, but they are not "us".

[Bored chemist]

Roughly speaking...
For any given shape, the area varies as the square of the height.
Computing power rises exponentially with time.
The cost of a given amount of computing power falls exponentially with time.
Current varies with the reciprocal. of resistance.
The typical instructions for time taken roasting meat are a linear, but not proportional function of time, but it's not proportional, because there's an offset.
20 minutes per pound  + 20 minutes.

And some are just plain silly.

heat cap eqn.png (13.31 kB . 787x247 - viewed 2146 times)

[alancalverd]

....which brings in the concept of hyperbolic expansion.

[Bored chemist]

I missed "factorially" off the list.
It's one of the few simple mathematical functions that rises faster than exponentially.
Among other things, it's the expression for the number of ways you can randomly assign n different letters to n addressed envelopes.
It is therefore, in some ways, the answer to "How many ways can things go wrong?".
You might have guessed that would rise quickly.
:-)

It's also interesting to see what that weird  equation I cited earlier is actually trying to model.
Here's the (measured) heat capacity of nitrogen vs temperature (K).
As you can see, to a reasonable precision, it is about 1.2


N2 heat cap.png (13.36 kB . 748x549 - viewed 2053 times)