Common Core Math: High School Functions: Linear & Exponential Models
High school students use linear and exponential models to describe mathematical relationships in the physical world. Linear models (of the form y = a × x + b) represent scenarios in which change is happening at a constant rate, while exponential models (of the form y = b × a<sup><i>x</i></sup>) represent scenarios in which the rate of change increases or decreases over time. Students learn to restate this distinction between linear and exponential functions in terms of different representations such as graphs, tables, equations, sequences and verbal descriptions. Students also learn to solve exponential equations, including by using logarithms.
Common Core Standards
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Construct Functions
Given a description, graph, table or sequence, construct linear and exponential models.
Construct linear functions (CCSS.Math.Content.HSF-LE.A.2):
Construct exponential functions (CCSS.Math.Content.HSF-LE.A.2):
Interpret components of linear and exponential functions (CCSS.Math.Content.HSF-LE.B.5):
Compare Functions
Explore similarities and differences between linear, polynomial and exponential functions.
Distinguish between linear and exponential functions (CCSS.Math.Content.HSF-LE.A.1):
Compare exponential functions to polynomials (CCSS.Math.Content.HSF-LE.A.3):
Solve Exponential Equations
Using logarithms, solve for a variable in the exponent of an expression.