## Process

__Part I: Population Estimates__Start by conducting Internet research to find global human population estimates from 1900 to 2010. Your years can count by any regular interval you like between 1s and 10s. That is, some groups might have tables that count by ones, {1900, 1901, 1902, … , 2010}, while others might count by 5s, {1900, 1905, 1910, 1915, … , 2010}, and other groups might count by 10s. Too much data can be overwhelming, while not having enough can make your growth model inaccurate. You will be using Google Spreadsheets. The video below will help you understand the functions of Google Spreadsheets.

Now that you know how to use Google Spreadsheets, you can start. Click here to go to Google Docs. Open a Google Spreadsheet. You will store your data here. It should look like this:

Answer these questions:

__Part 2: Finding a Good Growth Mode__

__l__Remember that population growth can be modeled in the

*short term*by where is your starting population when t = 0. If you want to find an exponential growth model, all you need is a starting point to call t = 0, and the associated population, , and an additional point of your choosing, . Using this, you can find a model P = P0ekt. With such a big data set, you can find many potential growth equations.

Remember that populations are best modeled by exponential growth when their growth is not inhibited by environmental factors. That is, populations are best modeled by exponential growth when there is not a scarcity of food, there is not a deadly disease pandemic, and there is not a devastating war taking place. Pick a year before 1965 to designate as t = 0 during which you believe the Earth’s population was growing exponentially.

Answer these questions:

4) Using the point (0,P0) you picked in Number 3, try various additional points, (t1,P1) to get different growth models P = P0ekt. Work with your partner to try as many as you can, and record the results in Google Spreadsheets similar to the table below:

6) Use your selected model to guess what the population was in 1960, 1980, 2000, and 2010. Compare to the actual values in a chart similar to this one:

8) Create a Google Spreadsheet to record Actual Growth versus your model’s Projected Growth as shown below. Make sure your first year is t = 0. To enter the equation P = P0ekt for the first cell of the projection, C3, you would write the following: =P0*exp(k*A2) where P0 and k are both numerical values you found. To fill in the entries below C3, you can use the Google Spreadsheet to fill cells. Replace my screenshot below with a screenshot of your model.

*(Note: The numbers I have included are purposefully inaccurate. You can’t use them.)*9) Use your model to extrapolate. You can obtain these values by extending your spreadsheet, or by plugging in for t in your model, P = P0ekt:

10) Use your Google Spreadsheet to create a chart that shows Actual Population Growth from your t = 0 until present and Projected Growth (Exponential Model) from your t = 0 until 2050. Make sure your axes are properly labeled and your chart is titled. Example below:

11) Use your Google Spreadsheet to create a chart that shows Actual Population Growth from your t = 0 until present and Projected Growth (Exponential Model) from your t = 0 until the year 3000. Make sure your axes are properly labeled and your chart is titled. Paste your chart over the example below:

**16) Within the confines of Planet Earth, there is a maximum human population that can live comfortably on the planet. This is called the carrying capacity, M, of the planet. Work with your partner to brainstorm as many different factors affecting the carrying capacity of the planet. You may do some additional research or talk to other groups to help you brainstorm:**

__Part 3: The Carrying Capacity of Planet Earth____Part 4: A Logistic Growth Model for Human Population Growth__

Recall that the logistic growth equation is where k is the growth constant, M is the carrying capacity, and A is a constant you solve for by plugging in (0,P0).

26) Use your Google Spreadsheet to create an assortment of charts comparing your Exponential Model to your Logistic Model (at least 3). Use different ranges for time along the x-axis to give a variety of different perspectives. Make sure your axes are properly labeled and your charts are titled.

27) Use your Google Spreadsheet to create a final chart of ONLY your Logistic Model from 30 years before t = 0 until the year 2100. Make sure your axes are properly labeled and your charts are titled.

28) Go compare with other groups! Go onto the blog and talk to other groups. Go under the Blog tab on the menu. The link is on this page. Find out what carrying capacities they picked:

28) Go compare with other groups! Go onto the blog and talk to other groups. Go under the Blog tab on the menu. The link is on this page. Find out what carrying capacities they picked:

**Part 5: Analyzing Rates of Change**Recall that if P(t)=M1+Ae-Mkt, then dPdt=kP(M-P).

**Part 6: Class Discussion about a World with M People**Our final task will be to discuss as a class what Earth might be like with M people on it.

__Topics__

· Production: agricultural techniques, sources of energy, architecture

· Usage: dietary choices, lifestyle choices

· Minimum Standard of Living: where do we set the minimum standard?

· Population Decline: trends in developed countries

· Further Learning: where does the model fall short?