MATH 164, Spring 2001 Due Date: Name(s):
Project 7.4a: Exponential Functions
Objective
To compare the behavior of various exponential functions.
Narrative
If you have not already done so, read Section 7.4 in the text.
In this project you will use the plot command to plot several functions on one set of coordinate axes.
These functions are important since they arise in applications that involve exponential growth (applications
such as population growth) and decay (applications such as radioactive decay and Newton's Law of Cooling).
Tasks
1. Type the command lines below into Maple in the order in which they are listed. These commands
produce graphs of y = ln x, y = exp x, and y = x to illustrate the inverse relationship of ln and exp.
> # Project 7.4a: Exponential Functions
> restart;
> plot({ln(x),exp(x),x},x=0..4,y=0..4,scaling=constrained);
2. Continue by typing the command lines below into Maple in the order in which they are listed. These
commands produce plots of the graphs of several exponential functions. The command that includes
the option scaling = constrained more accurately illustrates the actual range of values for ex
, e2x
,
and 2ex
.
> plot({exp(x),exp(2*x),2*exp(x)},x=-2..2,y=-1..30);
> plot({exp(x),exp(2*x),2*exp(x)},x=-2..2,y=-1..30,scaling=constrained);
> plot({exp(-x),exp(-2*x),2*exp(-x)},x=-1..3,y=-0.2..3);
> plot({1,1+exp(-x),1-exp(-x)},x=-1..3,y=-0.2..3);
At this point, make a hard-copy of your typed input and Maple's responses (both text and graphics).
Then continue with the following step.
3. Label by hand each of the curves in each of the graphics you created in parts (1) and (2). (For example,
label the graph of y = ex
by "y = ex
".)
Comments
You might find it instructive to repeat this project using bases such as 1/2, 2, and 10 rather than e, and
comparing the results.