Assignment 5: Using Differential Equations to Model Population Growth

Week 5

 

In class on Monday, [day 12]:

·        We will be working on Section 2.5: Modeling Population Growth.  I will give a short overview of the mathematical ideas in this section, and then let you work in groups to read this section and work through the Activities and Checkpoints.

o       Population growth is an example of a situation in which we are interested in looking at how things change.  This is the kind of problem for which Calculus is the ideal mathematical tool.  We will be using a new kind of tool: differential equations.

o       In Sections 2.3 and 2.4, we have been working with two fundamentally different families of functions.  In Section 2.5, we will focus on the family of differential equations whose solutions are exponential functions, functions of the form exponential

 

Before class on Wednesday, [day 13]:

·        Review Section 2.5: Modeling Population Growth, being sure that you understand what is going on in the Activities and Checkpoints.

·        Review the rules for calculating derivatives in Sections 2.3 and 2.4.

·        Review Section 1.5, particularly the ideas about logarithms and logarithmic functions.

 

In class on Wednesday, [day 13]:

·        We will be working on Section 2.6: Logarithms and Representation of Data.  Again, I will give a short overview of the mathematical ideas in this section, and then let you work in groups to read this section and work through the Activities and Checkpoints.

o       The principle new mathematical tools that are introduced in this section are logarithmic transformations of data, and log-log and semi-log plots. 

o       We will be working with logarithms and exponential functions, and with equations that are basically “linear equations.” 

o       You need to understand and be able to apply what is going on in the CAS worksheets of Section 2.6 in order to complete the Project.

 

In class on Friday, [day 14]:

·        The tools of Sections 2.5 and 2.6 give us some useful strategies for determining whether a given set of data (presented in a scatter plot) can best be modeled using a power function or an exponential function.  You will be able to apply these tools to solve the problems posed in Project 1: The Early Spread of AIDS in the US.  This project is spelled out in more detail on a separate handout.  This project will be due on Friday, September 25.

·        You may use class time on Friday to work on this project with your group and other class members.  You will need time outside of class next week to complete this project.