Introduction

Greetings Pre Calculus students!!  You are now at such an advanced stage of your high school math careers that letters are becoming numbers! As a class, we will be exploring and learning about the number "e" in a variety of ways. As individuals, you will learn the value of "e", graphs and limits associated with the number "e", and how we can use "e" in real world application. Teams of 4 will then role play a real life situation of city officials making future decisions based on population prediction using the number "e".  Students will assume the roles of either city mayor, city planner, county board member, or concerned citizen.

• Teams of 4 students will be videotaped in a mock city council meeting. The main focus of the meeting will be discussion on future growth of the city and implications regarding schools, annexation, and police/fire department increases. The city mayor will act as facilitator of the meeting. A citizen has issues that concern them such as raising property taxes and noise pollution in their quiet part of town. A county board member has concerns such as school district property alignment and one city's growth effecting the rest of the county.  The city planner will be in charge of taking existing population data and showing future growth based on the data.  The team must come to a consensus on decisions regarding 1 of 3 main issues: schools, annexation, and  police/fire. Prioritizing increasing budgets and rationalizing the decisions made using data will be crucial.  After reaching consensus, all team members will then make a formal presentation to the class on their findings.

Section 11:3 and 11:4 in your Pre Calculus book will be an excellent resource in helping you analyze population data and compute future population.  The number "e" will be instrumental in your mathematical formula for determining exponential growth.

Visualizing the growth rate on graphs will be very important when presenting information and making arguments for your points of view to visual people. This web site offers the user a chance to see how the "e" graph changes by changing variables with it. I highly recommend you visit this site when preparing for your exponential graphing quiz.

The number "e" is a key component in math formulas calculating population growth or rate of decay. The University of Toronto has a great web site for isolating the use of the number "e" in these math formulas. Struggling with the "math" part of calculating rates of change? This site would be a good one for you to visit prior to Mr. B's quiz on calculating rates of change using formulas.

The number "e" can be studied and used in regards to limits. In Pre Calculus, we will introduce this topic. Later in Calculus, limits will be studied in depth. For a preview of the number "e"" and its function with limits, click on this University of Toronto site. Local city council will be a valuable "people" resource.  Contact one city or county official and gain in-sight to this type of problem. Have a list of predetermined questions available for your city official prior to the contact. Use their experiences in similar situations that your team is facing as a resource to solving your population growth problems. Yorkville City Government.

• You will be first assigned to a team of 4 members. Your team will then decide on a fictitious city name to use for the rest of the project.
• Each team member will pick a role to play.  The 4 roles will be city mayor, city planner, county board member, and concerned citizen.
• Each team member will be given a hand-out showing past populations with their respective years. After receiving the hand-outs, team members should study the math component of using "e" in rate change formulas. (Refer to the resource section above)
• Team members should agree on a time and place to conduct their "mock" city council meeting. The meeting will be run by the city mayor and focus on the discussion of predicting future population numbers for their city. Using this data, the team will need to reach a consensus of prioritizing and increasing/maintaining/decreasing budgets in the areas of city annexation, police/fire department, and school district needs.  The teams need to videotape their "mock" meeting. Possible locations for the meeting include our library, conference room, or home. (Be creative!)  Length of meeting is not as important as what gets accomplished and discussion in the meeting.
• Math quiz in class on graphs and formulas with the number "e".
• Team presentation to rest of class. Your presentation will inform the class of your team's opinion regarding the impact of the predicted growth data effecting your city. Your presentation should also effectively justify your team's view on increasing, maintaining, or decreasing the city's annexation budgets based on math data.

Individually, you will be graded 2 ways:

1.) An individual 20 point quiz that  will evaluate your ability to use the value "e" in formulas to find
     solutions as well as to predict and analyze situations using rate of change formulas with the value
     "e".
        (state goal 6.A.5)

2.) A half page report on your personal contact with a city official.  A rubric for your report will be
      listed below.

As a team, you will be graded 2 ways:

1.) The videotape of your "mock" city meeting. A rubric for your video will be listed below.

2.) The team presentation.  A rubric for your team presentation will be listed below.

Illinois State Board of Education: State Goals

Using the number "e" in real life application is a prime example how upper level high school math can be incorporated in everyday life. By the end of this project, you will have learned what the numerical value of "e" is, how it is used in exponential growth equations, and how exponential graphs behave when constants are changed. You will also gain an understanding, and hopefully, an appreciation of use of team, people, and problem solving skills when faced with the challenge of reaching group consensus on a current issue. In an effort to model the importance of life long learning, any feedback to this project would be welcome.