Activity Overview
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.
Before the Activity
Open a new TI InterActive!™ document
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
Re-teach concepts as necessary