Pedagogy in Action > Library > Interactive Lectures > Examples > Effect of Proportionality Constant on Exponential Graph (k < 0)

Effect of Proportionality Constant on Exponential Graph (k < 0)

This page and activity authored by James Rutledge, St. Petersburg College. It makes use of an applet created by Larry Green, Lake Tahoe Community College, http://www.ltcconline.net/greenl/java/index.html
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This page first made public: Aug 19, 2010

This material was originally developed through Merlot as part of its collaboration with the SERC Pedagogic Service.

Summary

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k<0 and C is an arbitrarily fixed value in f(x)=Ce^(kx).

While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Learning Goals

To enable students to:

Context for Use

This activity can be carried out in either a small College Algebra class or a large lecture setting anytime during or after the topic of graphing exponential functions has been covered.

The activity is comprised of three segments: ConcepTest, Question of the Day and Conclusion, involving the use of a demonstration applet. The time required for the entire activity is approximately 25 minutes but fewer segments can be offered as a shorter alternative (see Activity Description below for individual segment times).

Description and Teaching Materials

Activity Description and Teaching Materials

Teaching Notes and Tips

Student understanding of the role of initial value and proportionality constant in exponential functions is limited at best. Most have not considered the y-intercept in terms of the values of C and k, and many have difficulty in analyzing the effects of changing the values of these terms. The fact that using a negative value for C reflects the graph around the x-axis seems to escape them. This activity is designed to help them develop a better grasp of the nature of exponential functions.

Assessment

I generally give the students a grade for participation in this activity and sometimes grade their final calculations concerning the work required.

References and Resources

Larry Green's Applet Page-Parameters and Graphs
This applet allows the user to change the initial value and the proportionality constant of an exponential function and immediately see the graphical results.
http://www.ltcconline.net/greenl/java/index.html
http://www.ltcconline.net/greenl/java/Other/MovingGraph/MovingGraph.html
MERLOT description of this resource
http://www.merlot.org/merlot/viewMaterial.htm?id=77279

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