Susan B. Batson email: sbbatso@ibm.net   Lesson Title: Investigating Exponential Functions Grade Level: Algebra II Length: Two Class Sessions Topic Covered: Exponential Functions  
1. Overview: This lesson introduces the exponential function through graphing and investigating patterns of graphs. Also connections are made to real-world applications.
 
2. Expected Outcome: The student will be able to graph exponential functions and relate these functions to the real world.
 
3. Background Information: Working knowledge of exponents, especially zero power, is necessary. Experience with using the graphing calculator is helpful.
 
4. Materials: Graphing Calculators, Catch 30 Video (Exponential Functions segment)
 
5. Standards:
1) Working with graphing calculators
2) Learning through investigations/identifying patterns
3) Cooperative learning/discussion
4) Real-World Applications of concepts
 
6. Five E's:
Engagement: Ask " What in nature multiplies or decays at a rapid rate?
Answers may include rabbits, amoebae, carbon-14, etc.
 
Exploration: Have students use the graphing calculator for the following equations:
  y = 1^x y = (2)^x y = (10)^x y = (1/4)^x y = (1/2)^x  
Explanation: Discuss patterns of graphs i.e. when the base is greater than 1, graph curves up, left to right;
when base is positive fraction, graph curves down, left to right; the larger the fraction, the closer the graph comes to the y = 1 line; the y-intercept is always = 1
 
Evaluation: Discussion; comparison of student graphs; homework; boardwork; quiz
 
Extensions: Use Catch 30 video to illustrate application of exponential functions i.e. reproduction, noise level, earthquake intensity. element decay, interest amortization
 
7. References: Catch 30 (Access Network) - Segment Two - Exponential and Logarithmic Functions