Back to Compare exponential and polynomial growth — Problem 2 · Task Set 57

HSF.LE.A.3 Tutor Intake — Exponential vs. Polynomial Growth

This short check helps your tutor understand where to start. Answer each question on your own. If you are not sure, give your best try — every response helps your tutor plan your sessions.

Grade 9·10 problems·~14 min·Common Core Math - HS Functions·group·hsf-le-a-3

Work through problems with immediate feedback

Concepts

A student says: "Since $x^2$ grows faster and faster (unlike
$x$ ), $x^2$ must be an exponential function."

What is wrong with this reasoning?

Nothing is wrong — $x^2$ does grow exponentially because its
rate of change increases.

Exponential functions require a constant multiplicative ratio
between consecutive values; $x^2$ does not have a constant
ratio.

$x^2$ cannot grow faster and faster because it is a polynomial.

Exponential functions must have integer bases, so $x^2$ is not
exponential only because 2 is the exponent, not the base.