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Fuel economy is a crucial concept when discussing vehicles and their efficiency. It refers to how far a car can travel per unit of fuel. It is most commonly expressed in miles per gallon (mpg). This measurement gives us an idea of the car's efficiency—how well it uses fuel compared to other vehicles. A higher mpg value means that the car can travel a longer distance on less fuel, which is great for saving on fuel costs and minimizing environmental impact.

In our example, the 2005 Mitsubishi Eclipse has a fuel economy of 26 mpg. This implies that on average, the car uses one gallon of gasoline to travel 26 miles. Understanding fuel economy is important for making informed decisions when purchasing a car, as well as planning trips to maximize fuel usage.

Proportionality is a mathematical concept that helps us understand relationships between different quantities. When we say two variables are proportionate, it means that as one variable changes, the other changes in a consistent way. In simpler terms, if you double one variable, the other also doubles, and so on.

In the case of fuel economy, we describe the relationship between distance traveled (D) and gasoline used (G) as directly proportional. The equation \( D = m \times G \) captures this relationship, where \( m \) is the constant of proportionality. Here, \( m \) is 26 miles per gallon, indicating that for each gallon of fuel, the car travels 26 miles. Understanding proportionality helps in predicting outcomes accurately based on variable changes.

Mileage calculation involves figuring out the total distance a vehicle can travel based on the amount of fuel consumed. Using the fuel economy as a constant of proportionality, we can determine how much distance can be covered with a specified amount of fuel.

For the Mitsubishi Eclipse, we use the formula \( D = 26 \times G \), where \( D \) is the distance traveled, and \( G \) is the gallons of gasoline used. If you know the gallons of gasoline available, simply multiply by 26 to find out how many miles you can drive. For example, with 2 gallons, the Eclipse can travel \( 26 \times 2 = 52 \) miles.

Identifying variables correctly is a fundamental step in solving mathematical problems involving functions. In our fuel economy exercise, the variables are clear: the amount of fuel used, denoted as \( G \), and the distance traveled, denoted as \( D \).

Recognizing that \( G \) represents gallons and \( D \) stands for distance allows us to apply the formula correctly. The constant \( m \), which is the fuel efficiency of the Eclipse at 26 miles per gallon, connects these variables within the function. Accurately identifying and understanding these variables is essential in creating and using mathematical models effectively in real-life applications.