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F-IF.9 Warmup M2-025-A07-V03

Compare function properties across representations, especially quadratic comparisons.

Compare two function values at the same input across representations

Problem

Compare \(A(t)=100(1.1)^t\) and \(B(t)=120+5t\) at \(t=2\). Evaluate the exponent before multiplying, substitute into the linear expression, and compare the numerical outputs without assuming one function family is always larger.

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A has the greater value because A(2)=100(1.1· 2)=220 and B(2)=130, so 220 is greater.

A has the greater value because it is exponential, so it must be larger than the linear function when t=2.

B has the greater value because A(2)=100(1.1)²=121 and B(2)=120+5(2)=130, and 130 is greater than 121.

The two functions have the same value because both are being compared at t=2, so A and B should match there.

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Curriculum context

Course: Math II
Standard: F-IF.9
Category: Functions
Domain: Interpreting Functions
Objective: Compare function properties across representations, especially quadratic comparisons.
Problem type: Compare two function values at the same input across representations