Exercises: Compare Exponential and Polynomial Growth

Work through each section in order. Show your work where indicated.

Grade 9·21 problems·~30 min·Common Core Math - HS Functions·group·hsf-le-a-3

Work through problems with immediate feedback

Warm-Up: Review What You Know

A student claims $h(x) = x^2$ grows exponentially because it gets faster and faster. Is the student correct?

Yes — $x^2$ accelerates (increases at an increasing rate), so it must be exponential.

No — exponential growth requires CONSTANT RATIOS between consecutive outputs. The ratios of $x^2$ are not constant.

Yes — any function that grows faster and faster is exponential.

No — $x^2$ does not get faster and faster; it grows at a steady linear rate.