Name____________________



Name____________________

CITY POPULATION REGRESSION

SUNRISE/SUNSET PROJECT

1. Choose a unique city.

2. Find the population for your city for the selected dates below.

|1910 | |

|1920 | |

|1930 | |

|1940 | |

|1950 | |

|1960 | |

|1970 | |

|1980 | |

|1990 | |

|2000 | |

3. Graph the data.

4. Use the data to find the following regression equations:

linear regression

quadratic regression

exponential regression

logarithmic regression

sine regression

5. Choose the best regression equation and use it to predict the population of the city in 2010. Look up the actual population in 2010. How close are the results?

6. Go to the website . Scroll down and click on the link on the left-hand side that says “Sunrise and Sunset Calculator”.

7. Choose a country and city to analyze. Write down the country and city here. Then click on “See sunrise/sunset”.

8. Use the drop-down menus to collect the data needed for the table below. Fill in the items on the first three columns of the table and calculate the fourth column.

| |Sunrise |Sunset |Length of Day |Length of Day |

| | | | |in minutes |

|January 1 | | | | |

|February 1 | | | | |

|March 1 | | | | |

|April 1 | | | | |

|May 1 | | | | |

|June 1 | | | | |

|July 1 | | | | |

|August 1 | | | | |

|September 1 | | | | |

|October 1 | | | | |

|November 1 | | | | |

|December 1 | | | | |

9. Complete the graphs. Make sure you include a title at the top of the page and a scale for each graph. Make your horizontal scale the same for each graph. Draw a smooth curve connecting your points on each graph.

10. Write down some of your observations about the three graphs.

11. Where are the maximum and minimum values of the three graphs? Explain why this is the case.

12. What is the standard form of a sine function?

13. On the length of day graph, what is a equal to? Write a brief description of what a is equal to, in general, for this project.

14. On the length of day graph, what is d equal to? Write a brief description of what d is equal to, in general, for this project.

15. What is the period for this data? Find the value of b using the formula: period = [pic].

16. What is the equation of your sine curve (so far)? Your answer should be in the form

y = a sin (bx) + d.

17. Use your calculator to find the sine regression equation for your data. Use numbers to represent the months (January = 1, February = 2, etc.). Write down this equation. How does this equation differ from the equation you wrote for question #9? How is this equation similar?

18. If the city you selected was closer to or farther away from the equator, how would your graphs be affected? How would your equation be affected? Be specific!

19. If the city you selected was the exact same distance on the other side of the equator, how would your graphs be affected? How would your equation be affected? Be specific!

[pic]

20.

Create a poster that summarizes your findings. Your poster needs to include the following:

• a title

• a table with the population data

• a graph of the population data

• the best-fit equation and curve on the graph

• the predicted population in 2020

• sunrise/sunset/length of day graphs

• sine regression equation for the length of day

• explanation of a and d

• a picture of your city

• an interesting fact about your city

• a map that shows the location of your city

-----------------------

Length of day (minutes)

Sunset

Sunrise

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