HS Math Concept: Linear, Quadratic, and Exponential Models

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Linear, Quadratic, and Exponential Models

Resources

Construct and compare linear, quadratic, and exponential models and solve problems.
HSF-LE.A.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. tools-icon
a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. tools-icon
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. tools-icon
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.  tools-icon
HSF-LE.A.2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).  tools-icon
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.  tools-icon
HSF-LE.A.4. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.  tools-icon
4.1 Prove simple laws of logarithms. CA  tools-icon
4.2 Use the definition of logarithms to translate between logarithms in any base. CA
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4.3 Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. CA  tools-icon
Interpret expressions for functions in terms of the situation they model.
HSF-LE.B.5. Interpret the parameters in a linear or exponential function in terms of a context.  tools-icon
6. Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. CA  tools-icon