Web Activities

CHAPTER 5 MODELLING PERIODIC FUNCTIONS

The Scenario

Your regional recreational department has hired you to develop a plan to optimize the creation of outdoor skating rinks in all of the surrounding town/city parks. As a climate consultant, you are expected to create a model that enables you to predict when the town should begin construction and flooding of the rinks. In addition, you are expected to report on the expected length of time the rinks should be able to remain operational. You are also asked to investigate the effects of Global Warming on creation of outdoor skating rinks in your community.

Use the Internet to gather data for the average monthly temperature of your community (or a community near yours).

Developing a Model

1. Create a table of values like the one that follows that lists the average temperature for each month in your community.

Average Temp.
(°C)

2. Assign every date of the calendar year a number, where January 1st corresponds to 1 and December 31st corresponds to 365. Add a row to your table that also displays the median day number for each month. Assume February always consists of 28 days.

3. Create a scatter plot of your data plotting Day Number vs. Average Temperature.
   
   
4. Draw the curve of best fit. Using transformations, determine an algebraic expression that models this curve.
   
   
5. Verify the accuracy of the model using the TI-83 Plus calculator and sinusoidal regression.
   

The Impact of Global Warming

Adjust the model to investigate the effects of Global Warming on the average monthly temperature. Environment Canada predicts that in Canada a further warming of 1° to 3.5° C, will occur over the next century. Increase the average monthly temperature by 2° C and determine the new model for your community

Your Job

Create a report that includes the following items:

• a table of the data you collected and the corresponding scatter plot you created.
• an explanation of how you used your knowledge of transformations to determine the algebraic equation of your curve of best fit.
• the equation of the algebraic model you determined.
• the equation of the algebraic model determined through sinusoidal regression.
• a paragraph that outlines to the recreational department the recommendations you are putting forward as to when to begin the creation of the outdoor rinks and the expected duration of a typical skating season. Justify any and all recommendations that you make.
• a model that takes into account the effects of a 2° C increase in the average monthly temperature due to global warming.
• a paragraph that outlines the impact this increase in temperature will have on the creation of outdoor skating rinks in your community.
  

Your report must be at least 500 words (approximately two double-spaced pages). You will be assessed on how well the report addresses the criteria mentioned above.