Exponential Functions Unit Plan

Introduction to Exponential Functions

General Outcome:  Develop algebraic and graphical reasoning through the study of relations.

SO5. Solve problems that involve exponential equations. [C, CN, PS, R, T]

5.1 Determine the solution of an exponential equation in which the bases are powers of one another; e.g., 2^x−1 = 4^x−2 .

5.2 Determine the solution of an exponential equation in which the bases are not powers of one another; e.g., 2^x−1 = 3^x+1 .

5.3 Solve problems that involve the application of exponential equations to loans, mortgages and investments.

5.4 Solve problems that involve logarithmic scales, such as the Richter scale and the pH scale.

SO6. Represent data, using exponential and logarithmic functions, to solve problems. [C, CN, PS, T, V]

6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its graph.
6.2 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its equation.
6.3 Match equations in a given set to their corresponding graphs.
6.4 Graph data, and determine the exponential or logarithmic function that best approximates the data.
6.5 Interpret the graph of an exponential or logarithmic function that models a situation, and explain the reasoning.
6.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of exponential or logarithmic functions, and explain the reasoning.

Additional physical world data sets that model the exponential function:

• National debt data,
• AIDS data,
• Money Growth and Investments,
• Ball bouncing,
• Creation of/and Analyzing Exponential Scatterplots in Excel or on a graphing calculator,
• Richter Scale, earthquakes,
• Bacteria Growth,
• Medicine in Blood Stream
• Population Growth

Prerequisite Skills

1.  Laws of Exponents Worksheet -- Rumbolt

Exploring the Characteristics of Exponential Functions

Achievement Indicators:

6.1 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its graph.

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Lesson Links: 

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

Exploring the Characteristics of Exponential Functions -- Youtube

Graphing Exponential Functions: Useful Patterns from Thinkwell Precalculus -- Youtube

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Additional Resources to Support this Lesson

• Purple Math:  Exponential Functions: Introduction
  

Discovery Based Learning

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Classroom Starter -- Crittenden

As an intro investigation, I like to talk about the fable of the inventor of chess. Apparently he was given the option of whatever prize he wanted. He wanted one grain of rice for the first square on the board, 2 for the second, 4 for the the next and so on. The grains of rice doubled for each square on the chess board.

The adjustment I make is I change it to pennies instead of rice, and offer the choice between the chess board prize or 1 billion dollars. You could even change this to 1 quadrillion dollars, and it's still not even close! Most students jump at the 1 billion dollars prize until they start playing with the numbers, and see how quickly the numbers grow.

If you keep it as a rice problem, you could talk about the plausibility of his demand. How large would a pile of this much rice be? What would this do to the Indian economy?

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1.  Click here for an interactive by Ron Blond to investigate the graphs of exponential functions.

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2.  Click here to download "Exploring What Exponential Functions Look Like" -- McInnes

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3.  Algebra 2: Graphing Exponentials -- Nspired Learning Math Classrom

Students will investigate the graphs of the family of exponential functions f(x) = b^x. As a result, students will:

• Infer why the conditions b > 0 and b ≠ 0 are necessary.
• Determine how the value of b affects the increasing or decreasing behavior of the function.
• Determine the y-intercept, domain, and range.
• Describe the end behavior.
• State the equation of the asymptote.

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Assessment for Learning

Relating the Characteristics of an Exponential Function to Its Equation

Achievement Indicators:

6.2 Describe, orally and in written form, the characteristics of an exponential or logarithmic function by analyzing its equation.
6.3 Match equations in a given set to their corresponding graphs.

______________________________________________________________________

Lesson Links:

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

Relating the Characteristics of an Exponential Function to Its Equation (Youtube)

Discovery Based Learning

Assessment for Learning 

Solving Exponential Equations

Achievement Indicators:

5.1 Determine the solution of an exponential equation in which the bases are powers of one another; e.g., 2^x−1 = 4^x−2 .

5.2 Determine the solution of an exponential equation in which the bases are not powers of one another; e.g., 2^x−1 = 3^x+1 .

______________________________________________________________________

Lesson Links:

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Discovery Based Learning

Assessment for Learning

1.  Solving Exponential Equations Sheet -- Rumbolt

2.  DO NOW Worksheet (Word Doc) 

Modelling Data Using Exponential Functions

Achievement Indicators:

6.4 Graph data, and determine the exponential or logarithmic function that best approximates the data.
6.5 Interpret the graph of an exponential or logarithmic function that models a situation, and explain the reasoning.
6.6 Solve, using technology, a contextual problem that involves data that is best represented by graphs of exponential or logarithmic functions, and explain the reasoning.

______________________________________________________________________

Lesson Links:

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Videos:

Modelling Data Using Exponential Functions -- Youtube

Discovery Based Learning

1.  PBS -- Math Line

Objective:  The objectives of this lesson are for students to explore the patterns of exponential models in tables, graphs, and symbolic forms and to apply what they have learned to make predictions in a real situation.

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2.  Contract For Employment -- Y. Chang

Objective: The idea is that you tell students they are going to work at job where they get paid $0.01 the first day, then double that each subsequent day.  You tell them they will work for 30 days total and ask them to make preductions about how much money they will make by the end.

Links for the activity that the idea is from as well as a handout given to students so that they could organize their work. 

Activity Link

Student Worksheet

Assessment for Learning

1.  Ipad Convincing -- Mini Performance Task  (anakamura.weebly.com/uploads/4/9/1/4/4914438/alg2y_pat.pdf‎)

2.  Donald Trump Problem -- Jayce Eifler

Financial Applications Involving Exponential Functions  

Achievement Indicators:

5.1 Determine the solution of an exponential equation in which the bases are powers of one another; e.g., 2^x−1 = 4^x−2 .

5.2 Determine the solution of an exponential equation in which the bases are not powers of one another; e.g., 2^x−1 = 3^x+1 .

5.3 Solve problems that involve the application of exponential equations to loans, mortgages and investments.

______________________________________________________________________

Lesson Links:

• Click here for a Notebook version of ERLC Lesson Link.  Please use this lesson as a framework for your own teaching environment.
• Click here for a pdf version of the same ERLC Lesson Link.

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Assessment for Learning

1.  Facebook Performance Assessment with Student Exemplars -- Click here

2.  Birthday Money Task (Word Doc)

Student Exemplars

Please feel free to share any student's work by emailing me at cketsa@gsacrd.ab.ca

Unit Shared Resources

Unit Notes:

1.  Exponential Functions Unit Notes -- Allen

2.  Teach21 Project Based Learning  Exponential Functions

WOW -- This is an amazing site for the entire unit. 

Summative Assessments

Click here to assess the summative assessment area. You will need an enrolment key to access this portion of the site.  Please email cketsa@gsacrd.ab.ca for access.

Below is a list of what is available for the Unit.

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Assignments

1.  Unit Assignment with Answer Key -- Ketsa

2.  Assign1 Exponential Functions  with Answer Key -- Williamson

Quizzes

1.  Chapter 6 Exponential Quiz with Answer Key -- Williamson

2.  Exponential Quiz with Answer Key -- Fowler

Exams

Performance Task

1.  Math 30-2 Performance Task Exponential with Answer Key -- Nagtegaal and Lambert