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Peer Review

Exponential Functions

by Philippe Laval


Overall Numeric Rating:

4 stars
Content Quality: 4 stars
Effectiveness: 4 stars
Ease of Use: 4 stars
Reviewed: Nov 29, 2004 by Mathematics
Overview: This site is a sub collection of a larger set by Philippe Laval containing a
variety of explorations. It is a self-contained collection of Java Applets that
can be used in the teaching and learning of mathematics.
Type of Material: Computation, graphics and simulation.
Recommended Uses: classroom demonstrations; student explorations
Technical Requirements: It requires a "Java-enabled" browser.
Identify Major Learning Goals: The Exponential Functions applet investigates the graph of an exponential
function as the base and coefficient change.
Target Student Population: Students in an intermediate or college algebra course.
Prerequisite Knowledge or Skills: The applets are self-explanatory and could easily be used by any mathematics
student without assistance, however may be most effective if preceded by an
instructor demonstration and explanation of terms.

Evaluation and Observation

Content Quality

Rating: 4 stars
Strengths: The Exponential Functions page contains one applet: ?Role of a and b?.

The ?Role of a and b? allows the user to enter values for a and b using a scroll
bar. The allowable values for the coefficient ?a? are ?10 to 9.9 and for the
base ?b? are 0.1 to 9.9. Accuracy to the tenth place is provided. As the
scroll bar is moved, the corresponding graph of y =a(b^x) is simultaneously
updated. Alternatively, the user may utilize Right or Left arrows at the ends
of the scroll bar to increase or decrease the values of ?a? or ?b.
Concerns: The scroll bar may be moved to select a value one for the base b. No error
message is provided that the definition of an exponential function excludes the
value of one as a base. The user instead sees a horizontal line on the screen,
concluding that the horizontal line y = 1 is an exponential function.

Potential Effectiveness as a Teaching Tool

Rating: 4 stars
Strengths: The ?Role of a and b? applet demonstrates effectively how changing the values of
the coefficient and base of an exponential function changes the shape of the
graph. Since the allowable values of ?a? include both negative and positive
values, and the allowable values of ?b? include those less than one and greater
than one, the user is able to experiment with various combinations of ?a? and
?b? to determine appropriate patterns.
Concerns: The applet does not provide background information on the mathematical concepts
or ask the students questions that would lead to specific conclusions. As a
result, the user must be given background information on the concepts to
effectively understand the purpose of the demonstration.

Ease of Use for Both Students and Faculty

Rating: 4 stars
Strengths: Students will need no explanation to use these applets, although there is an
itemized explanation available just below the applet. The scroll bar allows
easy entry of values for ?a? and ?b?. Right and left arrows on the scroll bar
assist the user in selecting specific values and consecutive values accurate to
the tenths place. The simultaneous appearance of the corresponding graph allows
the user to visualize the change in the graph that occurs as the values of ?a?
and ?b? are increased or decreased.
Concerns: The values shown for ?a? and ?b? are in textboxes that are not editable. Either
presenting these as labels or allowing the student to enter values and having
the graph adjust according to the entered values would make the applet more

Other Issues and Comments: