Exponential and Logarithmic Function Gallery

The following is a gallery of demos for illustrating selected families of functions These animations can be used by instructors in a classroom setting or by students to aid in acquiring a visualization background relating to the change of parameters in expressions for functions. Two file formats, gif and mov are available.

1. The gif animations should run on most systems and the file sizes are relatively small. 

2. The mov animations require the QuickTime Player (version 6) which is a free download available by clicking here; these files are also small. (The mov files may not execute properly in older versions of QuickTime.) 

3. The collection of animations in gif and mov format can be downloaded; see the 'bulk' zipped download category at the bottom of the following table.

4. We use abbreviations, GSP for Geometer's Sketch Pad 4, MAT for MATLAB, and EX for Excel spread sheet, to indicate the software used to generate the frames of the animation. If alternate corresponding software is also available there will be more than one abbreviation in that category. 

Exponential and Logarithmic Functions

General exponential function h(x)=ax   and f(x) = ax + b GSP also an EX file		Vary a: Gif Animation               Mov Animation Vary b: Gif Animation                Mov Animation
Exponential function base e h(x)=a ex+b   and f(x) = a ex+b + c GSP also an EX file		Vary a: Gif Animation               Mov Animation Vary b: Gif Animation               Mov Animation Vary c: Gif Animation               Mov Animation
Natural logarithm function h(x)=a ln(x+b)   and f(x) = a ln(x+b) + c GSP also an EX file		Vary a: Gif Animation               Mov Animation Vary b: Gif Animation                Mov Animation Vary c: Gif Animation               Mov Animation
Negative exponential family r(x) = a (1- e-bx )  GSP also an EX file		Vary a: Gif Animation              Mov Animation Vary b: Gif Animation                Mov Animation
Logistic equation family GSP also and EX file		Vary A: Gif Animation               Mov Animation Vary b: Gif Animation                Mov Animation Vary C: Gif Animation               Mov Animation
Normal density function GSP also and EX file		Vary a: Gif Animation                Mov Animation Vary b: Gif Animation                Mov Animation
Zipped downloads ==>	Download (all) the animations (large file) Download (6) Geometer's Sketch Pad files Down load (6) Excel files

Other Selected Resources:

• In the Math Archives at http://archives.math.utk.edu/visual.calculus/0/shifting.8/ are MathView notebooks to view graphically the effects of changing the coefficients a, b, c, and d in the exponential function f(x) = a e^{b (x - c)} + d.
  
  

• In the Math Archives at http://archives.math.utk.edu/visual.calculus/0/shifting.9/ are LiveMath notebooks to view graphically the effects of changing the coefficients a, b, c, and d in the exponential function f(x) = a ln(b (x - c)) + d.
  
  

• At http://www.bbc.co.uk/education/asguru/maths/13pure/05exposandlogs/25exponentials/25exponential.shtml the BBC education collection has a set of applets for exponentials and logarithms where you can change bases and parameters in expressions. 

Credits:

• The Geometer's Sketchpad routines were constructed by David R. Hill, Temple University, based on files contributed by Mark Yates of The McCallie School.

• The Excel files were constructed David R. Hill, Temple University.

• Special thanks to Deane Arganbright of University of Tennessee at Martin and to Walter Hunter at Montgomery County Community College for their assistance with the development of the Excel files that accompany this gallery. The book "Mathematical Modeling with Excel", by Erich Neuwrith and Deane Arganbright (Brooks-Cole) provides a rich source of information for developing Excel routines for mathematical instruction.

• This gallery was developed by David R. Hill, Temple University.