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Learning Goal
Part of: Construct and compare linear, quadratic, and exponential models and solve problems — 6 of 7 cluster items
Compare exponential and polynomial growth
HSF.LE.A.3
**HSF.LE.A.3**: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
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HSF.LE.A.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
What you'll learn
- Use tables of values to observe that an exponential function eventually produces larger outputs than any linear function, regardless of the linear function's slope
- Use tables of values to observe that an exponential function eventually produces larger outputs than any quadratic (or higher-degree polynomial) function
- Identify the crossover point where an exponential function overtakes a polynomial function by comparing values in a table or on a graph
- Explain in plain language why exponential growth dominates: multiplicative growth compounds while additive (or polynomial) growth does not
- Interpret graphs that show exponential and polynomial functions together, identifying regions where one exceeds the other
- Apply the dominance principle to real-world contexts (e.g., why compound interest eventually outpaces any fixed salary increase)
Prerequisites
Slides
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Slides
In development
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