# HS Math Concept: Linear, Quadratic, and Exponential Models

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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.
a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
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).
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.
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.
4.1 Prove simple laws of logarithms. CA
4.2 Use the definition of logarithms to translate between logarithms in any base. CA

4.3 Understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. CA
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.
6. Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity. CA