Here are population data for three cities at different times between 1950 and 2000. What does the data tell us, if anything, about the current population in the cities or what the population will be in 2050?
| City |
1950 |
1960 |
1970 |
1980 |
1990 |
2000 |
| Paris |
6,300,000 |
7,400,000 |
8,200,000 |
8,700,000 |
9,300,000 |
9,700,000 |
| Austin |
132,000 |
187,000 |
254,000 |
346,000 |
466,000 |
657,000 |
| Chicago |
3,600,000 |
3,550,000 |
3,400,000 |
3,000,000 |
2,800,000 |
2,900,000 |
- How would you describe the population change in each city during this time period? Write one to two sentences for each city. Then discuss with your group.
- What kind of model, linear or exponential, both, or neither do you think is appropriate for each city population?
- For each population that you think can be modeled by a linear and or exponential function:
- Write an equation for the function(s).
- Graph the function(s).
- Compare the graphs of your functions with the actual population data. How well do the models fit the data?
-
- Use your models to predict the population in each city in 2010, the current year, and 2050.
- Do you think that these predictions are (or will be) accurate? Explain your reasoning.
