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.
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.
Type of Material:
Computation, graphics and simulation.
classroom demonstrations; student explorations
It requires a "Java-enabled" browser.
Evaluation and Observation
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.
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
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.
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
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.
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 effective.