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F-LE.3 Core M2-026-R06-V04

Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.

Separate initial value from growth behavior

Problem

Compare \(Q(t)=100+2t^{2}\) and \(E(t)=100(1.20)^t\). Evaluate \(\text{both}\) at \(t=0\), identify the input power versus variable exponent, interpret \(1.20\) as a growth factor, and calculate \(Q(5)\) and \(E(5)\).

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Both start at 100; Q is quadratic and E grows by factor 1.20; Q(5)=150, E(5)=248.832.

Q starts at 2 and E starts at 1.20.

Q is exponential because both start at 100.

The models use different decay mechanisms.

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Curriculum context

Course: Math II
Standard: F-LE.3
Category: Functions
Domain: Linear, Quadratic, and Exponential Models
Objective: Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.
Problem type: Separate initial value from growth behavior