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F-LE.3 Core M2-026-R06-V03

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

Separate initial value from growth behavior

Problem

Compare \(A(t)=500(0.90)^t\) and \(B(t)=300(0.80)^t\). State each initial value, convert each multiplier to a percent decrease, and evaluate \(\text{both}~\text{models}\) at \(t=2\) while keeping coefficient and growth behavior distinct.

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Both models show growth.

The initial values are 0.90 and 0.80.

A has factor 0.50 and B has factor 0.70.

A starts at 500 and decays 10%; B starts at 300 and decays 20%; A(2)=405, B(2)=192.

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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