F-LE: Linear, Quadratic, and Exponential Models

Linear, Quadratic, and Exponential Models

Print

Linear, Quadratic, and Exponential Models focuses on recognizing which function family fits a given situation and constructing the appropriate model. Linear growth by equal differences and exponential growth by equal factors are contrasted directly. Parameters are interpreted in context, and models are used to predict, compare, and make decisions.

F-LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.F-LE.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or input-output table of values.F-LE.3Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.F-LE.4For 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.F-LE.5Interpret the parameters in a linear or exponential function in terms of a context.
Example Problems

Is
a solution to the above equation?

and


Solve the equation.
Maria and Lucia own land.

Lucia began with
11 hectares during the first month, and gained 5 more hectares each month.

Maria owned
6 hectares during the first one, and her land multiplied by a factor of each month.

After which month will Maria's amount of land first exceed Lucia's amount of land?
Evaluate:
Does the function model exponential growth or decay?
Goblins

1-on-1 AI tutoring aligned to F-LE. Instant help for students, real-time insights for teachers.

Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.

Free for teachers, forever →