Develop a model for the effective gas mileage (call it E) as a function of speed (S) for a ¡°typical¡± car (you should be able to find the necessary information to develop this model for your own car). This model should be valid for 55 ¡Ü S ¡Ü75 (it will be apparent from part a while a single function for all speeds would be difficult). State all of your assumptions.
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To develop a model for the effective gas mileage as a function of speed, you will need to gather information specific to your car. Here are the steps you can follow:
1. Gather data: Collect data on the gas mileage (miles per gallon) of your car at different speeds. You can do this by driving at different speeds and recording the gas mileage achieved.
2. Plot the data: Once you have the data, plot it on a graph with speed (S) on the x-axis and gas mileage (E) on the y-axis. This will help you visualize the relationship between the two variables.
3. Analyze the data: Observe the pattern in the plotted data. Does the gas mileage increase, decrease, or remain constant as speed changes? Note any significant changes or trends.
4. Determine the model: Based on the analysis of the plotted data, you can select an appropriate mathematical model that best represents the relationship between speed and gas mileage. Since the given range is 55 ≤ S ≤ 75, you may find that using multiple functions within this range is necessary.
5. State assumptions: Provide a clear statement of any assumptions you make during this modeling process. For example, you might assume that other factors, such as road conditions, vehicle maintenance, and driving habits, remain constant during the data collection process.
It's important to note that the model you develop will be specific to your car and may not be applicable to all cars. It's recommended to consult your car's user manual or reach out to the manufacturer for information regarding gas mileage at different speeds.