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M1-032-A07-V04
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F-LE.3
Warmup
M1-032-A07-V04
Use graphs/tables to see that exponential growth eventually exceeds linear, quadratic, and polynomial growth.
Choose a long-term model from accelerating changes
Problem
Analyze the displayed table to determine the function family and model, support the result with differences and ratios, give the growth rate per interval, and state the assumption required for long-term use.
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A
differences = 4,6,9, increase steadily; ratios = not used; family = linear; model = A(t)=8+4t; growth = add 4 per interval; assumption = differences remain 4
B
differences = 4,6,9; ratios = 1.5; family = exponential; model = A(t)=1.5·8ᵗ; growth = 50% per interval; assumption = factor 8 continues
C
differences = 4,6,9, not constant; ratios = 12/8=18/12=27/18=1.5; family = exponential; model = A(t)=8·1.5ᵗ; growth = 50% per interval; assumption = factor 1.5 continues for long-term prediction
D
differences = 4,6,9; ratios = 1.5; family = exponential; model = A(t)=8·1.5ᵗ; growth = 150% per interval; assumption = factor 1.5 continues
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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 Choose a long-term model from accelerating changes
