Problem preview

F-LE.3 Warmup M1-032-A02-V04

Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.

Compare quadratic and exponential values over the same inputs

Problem

Use the displayed table to compare \(Q\) and \(E\) at every listed input, identify the tie, and determine where \(E\) first overtakes \(Q\) among the listed integers.

Comparison table with rows x=0: Q=4, E=1; x=1: Q=9, E=4; x=2: Q=16, E=16; x=3: Q=25, E=64; x=4: Q=36, E=256.

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comparisons = x=0: Q>E; x=1: Q>E; x=2: tie at 16; x=3: Q>E because 25<64; x=4: E>Q; tie = x=2; first listed integer overtake = x=4

comparisons = x=0: Q>E; x=1: Q>E; x=2: tie at 16; x=3: Q>E; x=4: E>Q; tie = x=2; first listed integer overtake = x=4 because it is fourth position after x=0

comparisons = x=0: Q>E; x=1: Q>E; x=2: tie at 16; x=3: E>Q; x=4: E>Q; tie = x=2; exponential values = 2,8,16,32,64 despite nonconstant ratios

comparisons = x=0: Q>E; x=1: Q>E; x=2: tie at 16; x=3: E>Q; x=4: E>Q; tie = x=2; first listed integer overtake = x=3

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Curriculum context

Course: Math I
Standard: F-LE.3
Category: Functions
Domain: Linear, Quadratic, and Exponential Models
Objective: Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Problem type: Compare quadratic and exponential values over the same inputs