Mathematics » High School: Functions » Linear, Quadratic, & Exponential Models*

Construct and compare linear, quadratic, and exponential models and solve problems.

• 1. Distinguish between situations that can be modeled with linear functions and with exponential functions.

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  • Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

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  • Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

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  • Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

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• 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).

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• 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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• 4. For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

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Interpret expressions for functions in terms of the situation they model.

• 5. Interpret the parameters in a linear or exponential function in terms of a context.

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