Applied Calculus
Module 1 Final Project
Due Friday 1st February, 2008
Instructions
Your report for this project should be a typed paper. Mathematica output and
handwritten mathematical manipulations should either be included as figures within the
document or figures collected in an appendix and referred to explicitly in the text (e.g.
“see Figure 2 on page 5”). Do not print an entire Mathematica notebook; rather, copy the
relevant portions from Mathematica and paste them into your document.
Your group has been given a set of data and a list of potential functions to model
the data. Your report should model this data and investigate the model following the
outline of each of the lectures in this module. Your report should follow the outline
below, addressing each of the questions in each section. Graphs or mathematical
manipulations should be included as support, but are not sufficient to answer a question
without additional comments. You should aim to address each question definitively and
succinctly.
Outline
Paragraph I: Introduction
Write a short paragraph outlining the objective of this project (as described below).
Paragraph II: Qualitative Observations
Graph the data points. Describe the behavior of the data. From trends in the data, how
do you expect the values of the function to behave as x increases beyond points
represented by the data? Approximate the rate of change at each data point given (show
one or two computations in detail and collect the results of all of them in a table). How
accurate do you expect these computations to be?
Paragraph III: Model
Determine a formula for the function that models the data. Demonstrate how you
determined the values of the constants. Graph the function along with the data on the
same axes. As well, graph the function on a large enough interval of x-values so that you
can observe the long-term behavior. Discuss your predictions regarding the behavior of
the data as x increases.
Paragraph IV: Rate of Change Approximations
Using the techniques we have developed in class, approximate the rate of change of the
function at each of the given data points to a degree of accuracy with which you are
satisfied. Explain and demonstrate the approximation at one data point in detail and
collect the results in a table.
