F-LE.1.3

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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Formative Assessments
Formative Assessments
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Students are asked to compare a linear function and an exponential function in context.
Compare Linear and Exponential Functions
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Students are asked to compare a quadratic and an exponential function in context.
Compare Quadratic and Exponential Functions
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Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Data Flyer
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This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).
Equation Grapher
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Assessment Questions
Assessment Questions
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FSA Sample Question
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Videos of Expert Instruction
Videos of Expert Instruction
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Hook/Performance Tasks
Hook/Performance Tasks
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The purpose of this task it to have students discover how (and how quickly) an exponentially increasing quantity eventually surpasses a linearly increasing quantity. Students' intuitions will probably have them favoring Option A for much longer than is actually the case, especially if they are new to the phenomenon of exponential growth. Teachers might use this surprise as leverage to segue into a more involved task comparing linear and exponential growth.
Exponential growth versus linear growth I
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This problem solving task shows that an exponential function takes larger values than a cubic polynomial function provided the input is sufficiently large. This resource also includes standards alignment commentary and annotated solutions.
Exponential growth versus polynomial growth
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In this task students use verbal descriptions to construct and compare linear and exponential functions and to find where the two functions intersect (F-LE.2, F-LE.3, A-REI.11).
Population and Food Supply