Excel Level 1: Population Growth
High School
Concepts
Lesson Abstract
This lesson will introduce students to some of the basics of Excel and how to use formulas, slider bars, and graphs to create a model of population growth. This model will take into account factors such as birthrate and carrying capacity.
The students will guided to first build a simple linear growth model and they will then be taught how to change that into an exponential growth model, finally adding a carrying capacity to simulate an environment with limited resources.
Objectives
 Familiarize students with both basic and more advanced elements of Excel
 Introduce the concepts of a basic Population Growth model.
Key Terms
 Population Growth
 Linear Growth
 Exponential Growth
 Carrying Capacity
Prerequisite Knowledge
 Basic knowledge of Algebra (especially variables and functions)
 Some familiarity with Excel would be helpful, but not necessary
Teacher Preparation
The teacher will need to be familiar with some extra features of Excel beyond the most widely known. The Excel Tutorial can familiarize the teacher with these features:
 Naming Cells
 Formulas
 Slider Bars
 Graphs
You can see the Excel Tutorial here:
Download Document
You can also see the finished model here:
Download File
Materials
Required Materials  Media  Equipment 
 The Excel tutorial could be helpful for students but is not required
 
 Whiteboard and markers
 An overhead projector is recommended
 A computer for the teacher
 One computer for each student or pair of students)
 Each computer should be equipped with Microsoft Excel (preferably Excel 2004)

Safety
No safety issues in this lesson
Presentation Outline
 Introduction to the Population Growth Model (5 min)  Rabbit Cage  If want to find out how many rabbits will be in a cage after a few days, how can we figure it out? What can affect the size of the rabbit population?
 Increase in rabbits
 More rabbits are born
 Rabbits are added to the cage
 Decrease in Rabbits (We will not be dealing with a decrease in rabbits in this model)
 Rabbits die.
 Rabbits are taken from the cage
 If we know the number of rabbits today, how do we find out how many will be there tomorrow? (What information do we need?)
 How many rabbits are there?
 INITIAL = (Students provide)
 How many rabbits are added each day?
 Added Rabbits = (Students provide)
 HAVE = HAD + CHANGE
 Rabbits now = Rabbits yesterday + Added Rabbits

 Linear Growth (10 min)
 Create 2 columns
 In Column D, enter the names of the constants. In column E put the actual constants next to their labels and name the constants so you can refer to them by their names instead of their cell numbers.
 Initial Rabbits
 Added Rabbits
 Explain to students that constants must be named because the reference will stay the same... and it's much easier to remember names than rows and columns! Make sure to name the values rather than their labels.
 Enter values for Initial Rabbits and Added Rabbits
 Enter values in the first field in each column
 Day = 1
 Rabbits = Initial Rabbits (Click on the constant value!)
 Enter values in the next field of each column
 Day = 2
 Rabbits = Previous Rabbits (Click on the cell for day 1) + Added Rabbits (Constant value)
 Point out how the variable names show in the formulas
 Drag down values
 Select Day 1 and 2, drag down to 50
 Select Rabbits on Day 2, drag down to Day 50
 What happens if we change the constant for Initial Rabbits?
 This can be compared to a yintercept
 What happens if we change the constant for Added Rabbits?
 This can be compared to the slope
 Add scroll bars to Initial Rabbits and Added Rabbits.
 Add a graph

Physical Modeling and Measurement
 This lesson does not include Physical Modeling. 
 Exponential Growth (15 minutes)
 How do we find out how many rabbits will be born each day?
 A certain percent (birthrate) of the current number of rabbits
 Add birthrate to the constants (Name it!)
 Give birthrate a value (.1 or .2 are good values)
 Edit the Rabbits equation for day 2
 Rabbits = Previous Rabbits + Added Rabbits + (Prev Rabbits * Birthrate)
 This means that we are both adding a constant number of rabbits to the cage each day and some rabbits are being born each day.
 Drag Day 2 of Rabbits down
 Notice changes to the graph
 Should have an exponential curve going up
Carrying Capacity (15 minutes)
 Introduce Carrying Capacity
 What if there was a limit to the food supply?
 Any given environment can only support a certain number of animals.
 Equation for carrying capacity:
 (Prev Rabbits * Birthrate) * (Prev Rabbits / Carrying Capacity)
 Some of the baby rabbits can't survive.
 As Prev Rabbits gets closer to Carrying Capacity, less babies will survive because Prev Rab / Capacity approaches 1
 New equation:
 Prev R + Added_R + Prev R * Birthrate  (Prev R*Birthrate)*(Prev R/Capacity)
 Change equation for Rabbits in Day 2
 Drag down

 The students' finished model should look something like this:
Download File
Allow students to experiment with their models and make observations about the shape of the graph lines. Here are some example questions:
 Why does the graph line level off at the end?
 (carrying capacity, population can't spread beyond the limit)
 What could be added to this model to make it more realistic?
 How could scientists use this model?
 (Study the affects of different factors on a population)

 Use Excel II to teach the students about disease spread 
 