HSF-LE.A.3

[tomergal]

I wonder why the wording of the standard uses “observe.” Do we only want students to observe specific exponential functions exceeding specific polynomials? Don’t we want them to know that always happens (for increasing functions of course)? Shouldn’t they know, not only that it’s true, but why it’s true? Unfortunately, the progression doc doesn’t discuss this standard.

There are many informal ways to assure oneself of this property of exponentials over polynomials. However, I don’t want to go there without knowing it’s standard aligned, since this transgresses the apparent boundary outlined by the standard.

[Bill McCallum]

Here is the standard for convenience of other readers:

HSF-LE.A.3. Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.⋆

We certainly want students to know this is always true. However, the mathematical proof of this fact uses calculus, so it is beyond the scope of the standards. I don’t know what informal ways of seeing it you have in mind, but they may well fall under the rubric of “observe.”

[Author]

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