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

Fluency Practice

Can the exponential function $g(x) = 1.01^x$ eventually exceed $p(x) = x^{100}$ ?

No — the base 1.01 is too close to 1 for the exponential to ever catch up.

No — $x^{100}$ has such a high degree that no exponential can exceed it.

Yes — for any base $b > 1$ , the exponential $b^x$ eventually exceeds every polynomial, regardless of the polynomial's degree or coefficients.

Only if the base is at least 2.