Back to Compare exponential and polynomial growth — Problem 3 · Task Set 57

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

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

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Procedures

The table compares $p(x) = x^3$ and $g(x) = 2^x$ :

$x$	$p(x) = x^3$	$g(x) = 2^x$
8	512	256
9	729	512
10	1,000	1,024
11	1,331	2,048

Between which two consecutive integers does the crossover occur?

Between $x = 8$ and $x = 9$

Between $x = 9$ and $x = 10$

Between $x = 10$ and $x = 11$

There is no crossover; $x^3$ is always larger.