AP Calculus BC Practice Test

Which growth order correctly ranks exponential, polynomial, and logarithmic functions as x grows large?

Exponential, Polynomials, Logs Logs, Exponential, Polynomials Exponential, Logs, Polynomials Polynomials, Exponential, Logs

Correct Answer:

Exponential, Logs, Polynomials

Explanation:

When x gets really large, compare how fast each function goes to infinity. Exponential growth dominates every polynomial: for any base a > 1 and any positive n, the ratio a^x / x^n tends to infinity as x → ∞. So exponentials outrun polynomials. Next, polynomials outrun logarithms: for any n > 0, x^n / log x → ∞ as x → ∞. Therefore, the fastest to slowest among these is exponential, then polynomial, then logarithmic growth. The standard ranking from fastest to slowest is exponential, polynomial, logarithmic.

Access more questions from this quiz

Continue to AP Calculus BC Practice Test for more practice questions and the full quiz experience.

Access More Questions