Mathematical Analysis (Honors)
Unit 7: Logarithmic and Logistic Functions
In this unit, students build on their prior work with exponential functions to explore the logarithmic and logistic function families. Students revisit the concept of an inverse as they are introduced to logarithmic functions. Students apply properties of logarithms and exponents to solve logarithmic and logistic equations.
Students describe key features of the graphs of logarithmic and logistic functions, showing intercepts and end behavior, of logarithmic and logistic functions. They use transformations to sketch and analyze the graphs, focusing on domain and range restrictions. As the unit progresses, students build fluency with rewriting and/or identifying equivalent logarithmic expressions. Students solve realworld problems involving transformed logarithmic models, verify appropriateness of models, and make predictions based on the model.
Students describe key features of the graphs of logarithmic and logistic functions, showing intercepts and end behavior, of logarithmic and logistic functions. They use transformations to sketch and analyze the graphs, focusing on domain and range restrictions. As the unit progresses, students build fluency with rewriting and/or identifying equivalent logarithmic expressions. Students solve realworld problems involving transformed logarithmic models, verify appropriateness of models, and make predictions based on the model.
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Students will:
Use algebraic properties to write equivalent logarithmic equations.
MA.LF.A.1
Express the inverse of an exponential function as a logarithmic function and define the natural base.
MA.LF.A.2
Use the properties of logarithms, including change of base, to solve realworld and mathematical problems algebraically.
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F.IF.C.7.e
Graph logarithmic functions, showing intercepts and end behavior.
Apply understanding of logarithmic functions to solve realworld problems.
MA.LF.B.3
Sketch and analyze logarithmic functions and their transformations.
MA.LF.B.4
Solve exponential and logarithmic equations using logarithms.
Build and interpret logistic functions to model realworld problems.
MA.LF.C.5
Sketch and analyze logistic functions.
MA.LF.C.6
Compare and contrast the exponential, logarithmic, and logistic models.
MA.LF.C.7
Apply understanding of logarithmic and logistic functions to solve realworld problems.
Use algebraic properties to write equivalent logarithmic equations.
MA.LF.A.1
Express the inverse of an exponential function as a logarithmic function and define the natural base.
 Background Info.
 Check for Understanding: The Relationship Between Exponentials and Logarithms
 Review/Rewind: Evaluating Logarithms  e and Compound Interest
 Enrichment Tasks: Like This if You Want to be Wealthy  Exponential and Logarithms II
MA.LF.A.2
Use the properties of logarithms, including change of base, to solve realworld and mathematical problems algebraically.
 Background Info.
 Check for Understanding: Exponential Model Word Problems
 Review/Rewind: Medication Dissolves  Bacteria Growth  Intro to Logarithms  Change of Base
 Enrichment Tasks: Rise of Gas Prices
Analyze functions using different representations.
F.IF.C.7
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
 Background Info.
 Check for Understanding: Graphs of Logarithmic Functions
 Review/Rewind: Graph of Logarithms and Exponentials
 Enrichment Tasks: Logarithmic Graphs
F.IF.C.7.e
Graph logarithmic functions, showing intercepts and end behavior.
 Background Info.
 Check for Understanding: www.khanacademy.org/math/algebra2/exponentialandlogarithmicfunctions/graphsoflogarithmicfunctions/e/graphsofexponentialsandlogarithms
 Review/Rewind: Graphing Basic Logarithmic Functions
Apply understanding of logarithmic functions to solve realworld problems.
MA.LF.B.3
Sketch and analyze logarithmic functions and their transformations.
 Background Info.
 Check for Understanding: Graphs of Logarithmic Functions
 Review/Rewind:: Graphs of Logarithmic Functions
 Enrichment Tasks: Can You Hear Me Know?
MA.LF.B.4
Solve exponential and logarithmic equations using logarithms.
 Background Info.
 Check for Understanding: Solving Exponential Equations Using Logarithms
 Review/Rewind: Logarithmic Equations  Solving Exponential Equations Using Logarithms
 Enrichment Tasks: Carbon14 Dating in Practice II
Build and interpret logistic functions to model realworld problems.
MA.LF.C.5
Sketch and analyze logistic functions.
 Review/Rewind: Modeling Representations
MA.LF.C.6
Compare and contrast the exponential, logarithmic, and logistic models.
 Check for Understanding: Families of Functions Matching
 Enrichment Tasks: Domain and Range  Too Hot to Handle, Too Cold to Enjoy
MA.LF.C.7
Apply understanding of logarithmic and logistic functions to solve realworld problems.
 Background Info.
 Enrichment Tasks: Logistic Growth Model, Explicit Version
What are some signs of student mastery?

Tools & Technology
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