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M1-032-A08-V04
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F-LE.3
Warmup
M1-032-A08-V04
Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Interpret an overtaking point in context
Problem
Interpret the overtaking point of \(L\) and \(E\) in the displayed context graph. State the approximate equality and difference at the crossing, compare the models before and after it, and explain the estimate status for daily observations with the contextual units.
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A
at overtake = L(7)≈E(7); before = L>E before 7; after = E>L after 7; status = overtaking means growth rates, not totals, are equal; units = days and dollars
B
at overtake = L(7)=E(7)=7 dollars; before = L>E before 7; after = E>L after 7; status = exact because day 7 is labeled; units = days and dollars
C
at overtake = L(7)≈E(7) dollars and E-L≈0; before = L(d)>E(d) for modeled days before about 7; after = E(d)>L(d) for modeled days after about 7; status = day 7 is an approximate crossing, and daily observations may only bracket exact equality; units = days and dollars
D
at overtake = L(7)≈E(7); before = E>L before 7; after = L>E after 7; status = approximate; units = days and dollars
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Curriculum context
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 Interpret an overtaking point in context