Write Equations to Model Populations
Write Equations to Model Populations
Use the following prompt and table to answer questions 1 – 7.
The table below shows the population data for three cities at different times between 1950 and 2000.
| 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 |
- What does the data tell us, if anything, about the current population in the cities or what the population will be in 2050?
- 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, exponential, both, or neither) do you think is appropriate for each city's 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? Be prepared to show your reasoning.