In this activity, students collect population data for the world on 10 different days and then find a model for the data set assuming that over a short period of time the data can be considered linear. Finally, they evaluate the model over a much longer period to determine the validity of the linear model.

Record the day- population data from the United States Census bureau web page for 10 days including January, 1st

See the attached PDF file for detailed instructions for this activity

Print pages 34 - 38 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Enter the day number and population values into a list, and plot a graph of day number versus population

Choose two points that fit on the graphed line and record their coordinates

Use the coordinates to find the slope of the line that best fits the graphed data, and find the y- intercept

Using values of m and b form a linear model of the data and compare it to the graph to see how well it fits the data

Use the model to find the population on January 1st and compare it to the United States Census bureau data

Use the model to find the population on January 1, 2000 and also predict the year when the population was zero

Observe that the population calculated for January 1, 2000 by the linear model is too high, and the date of zero population is found to be 1920, which is not true

Observe that the model in the linear form is good only for data over a short period of time, and long term population predicting needs an exponential or logistic model

After the Activity

Review student results:

As a class, discuss questions that appeared to be more challenging