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Exponential Growth and Exponential Functions

Life Skills:

  • Thinking & Reasoning
  • Communication

Curriculum Tie:

Time Frame:
2 class periods that run 90 minutes each.

Group Size:
Small Groups


 

Summary:
Students will model exponential growth and explore graphing exponential functions through transformations.

Main Curriculum Tie:
Secondary Mathematics I
Strand: FUNCTIONS - Building Linear or Exponential Functions (F.BF) Standard F.BF.3

Identify the effect on the graph of replacing f(x) by f(x) + k, for specific values of k (both positive and negative); find the value of k given the graphs. Relate the vertical translation of a linear function to its y-intercept. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

Background For Teachers:
This lesson is broken into two parts.

Part I requires students to fit an exponential model to a specific situation. They explore the domain and range of this model.

Part II leads students to draw conclusions about transformations of exponential functions.

Student Prior Knowledge:
Students need to know how to graph ordered pairs, basic properties of exponents, and be able to recognize function notation.

Intended Learning Outcomes:
The numbers below correspond to the Intended Learning Outcomes from the secondary math core.

2. Become proficient problem-solvers by posing appropriate questions, selecting appropriate methods, employing a variety of strategies, and exploring alternative approaches.

3. Think logically, using inductive reasoning to formulate reasonable conjectures and using deductive reasoning for justification, formally or informally.

4. Cooperatively and independently explore mathematics, using inquiry and technological skills.

6. Communicate mathematics through writing, modeling, and visualizing, using precise mathematical language and symbolic notation.

Instructional Procedures:
The worksheet provided can serve as the introduction to modeling and graphing exponential functions. It is not expected that students will have been taught any specifics about exponential functions or their graphs.

The lesson starts with students receiving copies of the worksheet. The teacher should help the students understand the situation described in Part I. Students should then be able to work together in small groups to complete Part I of the worksheet. A discussion should be held once Part I is complete. Make sure to discuss the equations students used to model the situation, as this is a fundamental idea for Part II.

The "Exponential Transformations" web site below provides an applet where students can change the values of a, b, h, and k and see what effect this has on an equation. They can use this to help them graph the functions, or they can graph the functions by filling in the table.

Attachments

Web Sites

Author:
Wendy Harmon
Richard Stewart

Created Date :
Oct 02 2007 14:10 PM

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