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Chapter 5--Exponential, Power and Logarithmic Functions

Essential Question:  How are the properties, graphs, and application of inverse functions, exponential and logarithmic, alike and how are they different?

Unit Rationale:  Reviewing properties of exponents, writing explicit formulas for geometric sequences, using rational exponents, finding inverse of a function, and understanding relationships between a function and it inverse all lead to solving real-world problems involving growth and decay.

As a result of this unit, students will be able to:

Ø  Know and use properties of exponents

Ø  Write explicit equations for geometric sequences as the lead-in to exponential equations

Ø  Simplify radical expression

Ø  Solve power equations

Ø  Set up and solve exponential equations from a situation

Ø  Graph exponential equations

Ø  Understand logarithms as a method for solving exponential equations

Ø  Understand and apply log rules

Ø  Understand relationships between tables, graphs, and equations for exponential equations

Ø  Write exponential equations from tables and graphs


·         Exponential functions

·         Properties of exponents

·         Power function

·         Rational exponent

·         Inverse

·         Logarithm

·         Common logarithm

·         Logarithmic function

·         Properties of logarithms

·         Base

·         Asymptotes

·         Explicit formula

Focus Standards:

A2.1.D  solve problems that can be represented by exponential and logarithmic functions and equations

A2.2.B  Use the laws of exponents to simplify and evaluate numeric and algebraic expressions that contain rational exponents

A2.4.A  Know and use basic properties of exponential and logarithmic functions and the inverse relationship between them.

A2.4.B  Graph an exponential function of the form f(x)=ab^x and its inverse logarithmic function

A2.4.C  Solve exponential and logarithmic equations

Support Standards:

A2.1.A  Select and justify functions and equations to model and solve problems.

A2.1.B  Solve problems that can be represented by systems of equations and inequalities.

Reasoning, Problem Solving, and Communication Standards:

A2.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.

A2.8.C  Evaluate a solution for reasonableness, verify its accuracy, and interpret the solution in the context of the original problem.

A2.8.F  Summarize mathematical ideas with precision and efficiency for a given audience and purpose.

A2.8.B  Select and apply strategies to solve problems

A2.8.G  Use inductive reasoning and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures.