F-LE. Linear, Quadratic, and Exponential Models

• All Your Base Are Belong to Us

F-LE.A. Construct and compare linear, quadratic, and exponential models and solve problems.

• Comparing Exponentials
• Comparing Graphs of Functions
• Dido and the Foundation of Carthage
• Extending the Definitions of Exponents, Variation 2
• Rising Gas Prices – Compounding and Inflation
• Triangular Numbers
• What functions do two graph points determine?

F-LE.A.1. Distinguish between situations that can be modeled with linear functions and with exponential functions.

• Basketball Bounces, Assessment Variation 1
• Basketball Bounces, Assessment Variation 2
• Boiling Water
• Choosing an appropriate growth model
• Exponential Functions
• Interesting Interest Rates
• Linear or exponential?

F-LE.A.1.a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

• Equal Differences over Equal Intervals 1
• Equal Differences over Equal Intervals 2
• Equal Factors over Equal Intervals

F-LE.A.1.b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

• Finding Linear and Exponential Models
• Identifying Functions
• In The Billions and Linear Modeling
• Linear Functions
• Solving Problems with Linear and Exponential Models
• US Population 1982-1988

F-LE.A.1.c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

• Algae Blooms
• Basketball Rebounds
• Carbon 14 Dating, Variation 2
• Finding Linear and Exponential Models
• Identifying Functions
• Illegal Fish
• In the Billions and Exponential Modeling
• Solving Problems with Linear and Exponential Models
• U.S. Population 1790-1860

F-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).

• Algae Blooms
• Allergy medication
• A valuable quarter
• Basketball Bounces, Assessment Variation 1
• Basketball Bounces, Assessment Variation 2
• Basketball Rebounds
• Boiling Water
• Boom Town
• Carbon 14 dating in practice II
• Choosing an appropriate growth model
• Decaying Dice
• Do two points always determine a linear function?
• Do two points always determine a linear function II?
• Do two points always determine an exponential function?
• Exponential Parameters
• Finding Parabolas through Two Points
• F-LE, A-CED Paper Folding
• Identifying Exponential Functions
• Moore's Law and Computers
• Population and Food Supply
• Predicting the Past
• Rumors
• Sandia Aerial Tram
• Snail Invasion
• Temperatures in degrees Fahrenheit and Celsius
• Two Points Determine an Exponential Function I
• Two Points Determine an Exponential Function II

F-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.

• Exponential growth versus linear growth I
• Exponential growth versus linear growth II
• Exponential growth versus polynomial growth
• Population and Food Supply

F-LE.A.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.

• Accuracy of Carbon 14 Dating II
• Algae Blooms
• Bacteria Populations
• Carbon 14 dating
• Carbon 14 dating in practice II
• Exponential Kiss
• Graphene
• Newton's Law of Cooling
• Snail Invasion

F-LE.B. Interpret expressions for functions in terms of the situation they model.

F-LE.B.5. Interpret the parameters in a linear or exponential function in terms of a context.

• A Saturating Exponential
• Carbon 14 dating in practice I
• DDT-cay
• Illegal Fish
• Newton's Law of Cooling
• Taxi!
• US Population 1982-1988