Chapter 6—Exponents and Exponential Models

Essential Question:  How do we model and solve real problems of exponential growth or decay and how are those models different from those of linear data?

Unit Rationale:  Modeling exponential growth and decay helps us understand real-world situation such as financial investments, population growth, and radioactive decay.  Prior units have focused on a constant rate of change (repeated addition), while this unit introduces increasing or decreasing rate of change through repeated multiplication.

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

Ø  Model exponential growth or decay using the form y=ab^n

Ø  Apply properties of exponents, including multiplication, division, and power properties to simplify exponential expressions and solve exponential equations.

Ø  Use scientific notation to represent large or small numbers

Ø  Find starting value, multiplier, and nth term of a geometric sequence.

Vocabulary:

·        Exponential equation

·        Exponential function

·        Exponential Growth

·        Exponential Decay

·        Properties of exponents

·        Scientific notation

·        Multiplier

Standards: Standards will be assessed on both the state and classroom levels, however, standards with an asterisk (*) in the code will count for graduation requirements. 

Focus Standards:

*A1.1.E  solve problems that can be represented by exponential functions and equations.

Supporting Standards:

*A1.2.C  Interpret and use integer exponents and square and cube roots, and apply the laws and properties of exponents to simplify and evaluate exponential expressions.

*A1.7.A  Sketch the graph for an exponential function of the form y=ab^n where n is an integer, describe the effects that changes in the parameters of a and b have 0on the graph and answer questions that arise in situations modeled by exponential functions.

Reasoning, Problem Solving, and Communication Standards:

A1.8.D  Generalize a solution strategy for a single problem to a class of problems and apply a strategy for a class of related problems to solve specific problems.

A1.8.E  Read and interpret diagrams, graphs, and text containing the symbols, language and conventions of mathematics.

A1.8.H  Use inductive reasoning about algebra and the properties of numbers to make conjectures, and use deductive reasoning to prove or disprove conjectures.