# 10.3: Activities and Answer Keys

**At Grade**Created by: CK-12

## Activity 9-1: Brush Rabbit Boom

### PLAN

** Summary** Students learn about population growth by analyzing two scenarios in the life of a brush rabbit population.

*Objectives*

Students:

\begin{align*}\checkmark\end{align*} distinguish between linear growth and exponential growth patterns.

\begin{align*}\checkmark\end{align*} organize information to be presented in graph format.

*Student Materials*

- Resource
- Data Sheet: Graph A
- Data Sheet: Graph B
- Activity Report
- Pencils
- Graph paper (optional)

*Teacher Materials*

- Activity Report Answer Key

*Advance Preparation*

None

** Estimated Time** One 50-minute period

*Interdisciplinary Connection*

**Math** Students create and analyze graphs in this activity.

*Prerequisites and Background Information*

Students should have some basic graphing skills.

Growth rates can be characterized by two different kinds of growth curves.

- Linear growth increases by a constant amount over time. Graph A in this activity demonstrates linear growth.
- Exponential growth increases by a constant proportion over time. Graph B in this activity demonstrates exponential growth.

### IMPLEMENT

** Introduce Activity 9-1** by reviewing basic graphing skills with students. To present the ideas of constant growth and increasing growth, compare what happens when you put $10.00 per month into a bank account with compound interest and $10.00 per month in a piggy bank. The bank account demonstrates increasing growth (exponential). The amount of money in the piggy bank demonstrates constant growth (linear).

** Steps 1-3** Make sure students complete the graphs in Part A and Part B so that they have a basis for comparing the different types of growth. You may want to have students answer the Activity Report questions individually in class or as homework.

** Conclude Activity 9-1** by discussing the graphs with the whole class. Ask students to explain what the graphed trends indicate about the brush rabbit population.

### ASSESS

Use the students' graphs and written answers to assess if students can

\begin{align*}\checkmark\end{align*} present information in a graph format.

\begin{align*}\checkmark\end{align*} explain the differences between a linear growth pattern and an exponential growth pattern.

## Activity 9-1 Brush Rabbit Boom Data Sheet: Graph A Answer Key

- Sample answers to these questions will be provided upon request.
**Please send an email to teachers-requests@ck12.org to request sample answers.**

- Summarize your data below.
- On the graph below, plot the population growth of brush rabbits over five years when some coyotes were killed by ranchers. Graph the data on the graph below.

## Activity 9-1 Brush Rabbit Boom Data Sheet: Graph B Answer Key

- Sample answers to these questions will be provided upon request.
**Please send an email to teachers-requests@ck12.org to request sample answers.**

- Summarize your data below.
- On the graph below, plot the population growth of brush rabbits over a five-year period when most of the predators have been eliminated. Graph the data on the graph below.

## Activity 9-1: Brush Rabbit Boom – Activity Report Answer Key

- Sample answers to these questions will be provided upon request.
**Please send an email to teachers-requests@ck12.org to request sample answers.**

- Which graph shows the most rapid increase in population growth? Explain.
- Study the growth curve in Graph A.
- What type of growth curve is represented in Graph A? Explain.
- Predict what would happen to the brush rabbit population five years from now if the conditions remain unchanged.

- Study the growth curve in Graph B.
- What type of growth curve is represented in Graph B? Explain.
- An ecologist surveyed 7,635 brush rabbits after the five years. Give a reason why there is a difference between the ecologist's number and the number plotted on the graph at year 5.

- Refer to the graph on the Activity 9-1 Resource, which shows human population growth. There are now more than 6 billion people in the world, and the human population is expected to double in about 40 years. Why should we be concerned with human population growth?

A suggested response will be provided upon request. **Please send an email to teachers-requests@ck12.org.**

How many calories are there in 300 gigajoules?

Suppose you wanted to reduce the amount of resources humans consumed in an area.

- Explain one strategy to keep the number of people in the area from growing.
- Explain one strategy to reduce the amount of resources that each person used.
Which countries would you advise to use each strategy?

A suggested response will be provided upon request. **Please send an email to teachers-requests@ck12.org.**

Suppose that the world's population doubles in 40 years, and energy consumption rates remain the same. What percentage of the world's net primary productivity will be used by humans in 40 years? What percentage will be left over for all of the other living things on Earth?

## Review Questions/Answers

- Sample answers to these questions will be provided upon request.
**Please send an email to teachers-requests@ck12.org to request sample answers.**

- What is a population? What are four ways in which its size may change?
- Suppose the doubling time for a population of algae in a pond is 24 hours. Also suppose the pond is now at capacity for algae. How long ago was the pond only half full of algae? How long ago was the pond one-fourth full of algae?
- Is the size of the world's human population growing or shrinking? Is it doing this at a constant rate?
- Do 100 people living in developing countries such as Nigeria have the same impact on the environment as 100 people living in the United States? Explain your answer.

## Activity 9-1 Data Sheet: Graph A Brush Rabbit Boom (Student Reproducible)

1. Summarize your data below.

\begin{align*}& \qquad \qquad \text{Year} && \qquad \qquad \text{Number}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

2. On the graph below, plot the population growth of brush rabbits over a five-year period when some coyotes were killed by ranchers.

## Activity 9-1 Data Sheet: Graph B Brush Rabbit Boom (Student Reproducible)

1. Summarize your data below.

\begin{align*}& \qquad \qquad \text{Year} && \qquad \qquad \text{Number}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\\ &\underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;} && \underline{\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}\end{align*}

2. On the graph below, plot the population growth of brush rabbits over a five-year period when most of the predators have been eliminated.

## Activity 9-1 Resource: Brush Rabbit Boom (Student Reproducible)

The graph shows the approximate growth of the world's population since 8000 BC. The line wobbles up and down but basically stays flat from 8000 BC until after AD 1000. Then all of a sudden the population starts to increase dramatically. The graph shows that it took thousands of years for the human population to reach 1 billion. Then it took 130 years to reach 2 billion, 30 years to reach 3 billion, and 15 years to reach 4 billion. Then it took only 13 years to reach 5 billion. How many years did it take to go from 5 billion to 6 billion?

## Activity 9-1 Report: Brush Rabbit Boom (Student Reproducible)

1. Which graph shows the most rapid increase in population growth? Explain.

2. Study the growth curve in Graph A.

a. What type of growth curve is represented in Graph A? Explain.

b. Predict what would happen to the brush rabbit population five years from now if the conditions remain unchanged.

3. Study the growth curve in Graph B.

a. What type of growth curve is represented in Graph B? Explain.

b. An ecologist surveyed 7635 brush rabbits after the five years. Give a reason why there is a difference between the ecologist's number and the number plotted on the graph at year 5.

4. Refer to the graph on Activity 9-1 Resource, which shows human population growth. There are now more than 6 billion people in the world, and the human population is expected to double in about 40 years.

Why should we be concerned with human population growth?

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