Alaska: Linear, Quadratic, and Exponential Models Math Standards

DISTINGUISH BETWEEN SITUATIONS THAT CAN BE MODELED WITH LINEAR FUNCTIONS AND WITH EXPONENTIAL FUNCTIONS.

• F-LE.1.a Show that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
• F-LE.1.b Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
• F-LE.1.c Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

CONSTRUCT LINEAR AND EXPONENTIAL FUNCTIONS, INCLUDING ARITHMETIC AND GEOMETRIC SEQUENCES, GIVEN A GRAPH, A DESCRIPTION OF A RELATIONSHIP, OR INPUT-OUTPUT TABLE OF VALUES.

OBSERVE USING GRAPHS AND TABLES THAT A QUANTITY INCREASING EXPONENTIALLY EVENTUALLY EXCEEDS A QUANTITY INCREASING LINEARLY, QUADRATICALLY, OR (MORE GENERALLY) AS A POLYNOMIAL FUNCTION.

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.

INTERPRET THE PARAMETERS IN A LINEAR OR EXPONENTIAL FUNCTION IN TERMS OF A CONTEXT.