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F-IF.9 Warmup M3-028-A08-V02

Compare functions represented algebraically, graphically, numerically, or verbally.

Compare the long-term behavior of polynomial and exponential functions across representations

Problem

How does the long-term behavior of these functions compare: \(f(x)=100x^5\) and \(g(x)=1.01^x\)?

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As x gets very large, 100x⁵ grows faster forever because the coefficient 100 and the fifth power make it stronger than 1.01ˣ.

As x gets very large, 100x⁵ and 1.01ˣ have the same long-term behavior because both keep increasing and can be large for big x-values.

100x⁵ may be larger for a while, but as x gets very large, 1.01ˣ eventually outgrows it because exponential growth beats polynomial growth.

As x gets very large, 1.01ˣ grows slower forever because its base is so close to 1, so 100x⁵ will always stay larger.

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Curriculum context

Course: Math III
Standard: F-IF.9
Category: Functions
Domain: Interpreting Functions
Objective: Compare functions represented algebraically, graphically, numerically, or verbally.
Problem type: Compare the long-term behavior of polynomial and exponential functions across representations