Problem preview

F-LE.3 Warmup M2-026-A04-V01

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

Identify and verify the first overtaking row

Problem

Locate the first overtaking row in this complete table: \(n=0,1,2,3,4\); \(A=5,10,20,40,80\); \(B=30,35,40,45,50\).

Source table: n=0,1,2,3,4; A=5,10,20,40,80; B=30,35,40,45,50.

Big Picture

What this problem is really about

The word first turns an overtake into an ordered-search problem. We’ll scan same-input comparisons from left to right, find the first strict reversal, and verify the immediately preceding row still has the old ordering.

Answer choices

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A first exceeds B at n=4: 80>50, after 40<45 at n=3.

A first exceeds B at n=3 because A(3)=B(2)=40.

B overtakes A at n=0.

A first exceeds B at n=5.

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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: Identify and verify the first overtaking row