9.2.3: Using and Interpreting a Mathematical Model
- Page ID
- 38068
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Lesson
Let's use a model to make some predictions.
Exercise \(\PageIndex{1}\): Using a Mathematical Model
In the previous activity, you found the equation of a line to represent the association between latitude and temperature. This is a mathematical model.
- Use your model to predict the average high temperature in September at the following cities that were not included in the original data set:
- Detroit (Lat: 42.14)
- Albuquerque (Lat: 35.2)
- Nome (Lat: 64.5)
- Your own city (if available)
- Draw points that represent the predicted temperatures for each city on the scatter plot.
- The actual average high temperature in September in these cities were:
- Detroit: \(74^{\circ}F\)
- Albuquerque: \(82^{\circ}F\)
- Nome: \(49^{\circ}F\)
- Your own city (if available):
How well does you model predict the temperature? Compare the predicted and actual temperatures.
- If you added the actual temperatures for these four cities to the scatter plot, would you move your line?
- Are there any outliers in the data? What might be the explanation?
Exercise \(\PageIndex{2}\): Interpreting a Mathematical Model
Refer to your equation for the line that models the association between latitude and temperature of the cities.
- What does the slope mean in the context of this situation?
- Find the vertical and horizontal intercepts and interpret them in the context of the situation.
- Can you think of a city or a location that could not be represented using this same model? Explain your thinking.