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According to a​ study, a​ vehicle's fuel​ economy, in miles per gallon​ (mpg), decreases rapidly for speeds over

45
 
mph.

​a) Estimate the speed at which the absolute maximum gasoline mileage is obtained.

​b) Estimate the speed at which the absolute minimum gasoline mileage is obtained.

​c) What is the mileage obtained at

90
 
​mph?

Question content area bottom left

Part 1

​a) The speed at which the absolute maximum gasoline mileage is obtained is approximately

enter your response here

mph.

mph.

mpg.

​(Type a whole​ number.)

Let's analyze the graph and answer each part based on visual inspection and estimation.

### a) Absolute Maximum Gasoline Mileage
To find the speed at which the absolute maximum gasoline mileage occurs, we look for the highest point on the curve. From the graph, this peak appears to be around **45 mph** on the horizontal (speed) axis. At this point, the fuel economy (mileage) reaches its maximum value, which looks to be around **36 mpg**.

**Answer for (a):** The speed at which the absolute maximum gasoline mileage is obtained is approximately **45 mph**.

### b) Absolute Minimum Gasoline Mileage
For the absolute minimum gasoline mileage, we need to find the lowest point on the curve. Observing the graph, it seems that the lowest fuel economy value occurs at the right end of the curve, around **90 mph**.

**Answer for (b):** The speed at which the absolute minimum gasoline mileage is obtained is approximately **90 mph**.

### c) Mileage at 90 mph
At 90 mph, the fuel economy (mileage) appears to be near **6 mpg** on the vertical axis.

**Answer for (c):** The mileage obtained at **90 mph** is approximately **6 mpg**.

Would you like further details on the interpretation or calculations?

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Here are five follow-up questions to deepen your understanding:

1. What type of function might model the relationship between speed and fuel economy in this graph?
2. Why does fuel economy generally decrease at higher speeds?
3. How would the graph look if this vehicle had a different fuel economy pattern?
4. Can calculus be used to find the exact maximum and minimum values on a fuel economy graph?
5. How could we estimate the fuel economy for speeds not directly shown on the graph?

**Tip:** For better accuracy, graphs like this can be analyzed with quadratic models if they follow a parabolic shape.

According to a study, a vehicle's fuel economy, in miles per gallon (mpg), decreases rapidly for speeds over 45 mph. a) Estimate the speed at which the absolute maximum gasoline mileage is obtained. b) Estimate the speed at which the absolute minimum gasoline mileage is obtained. c) What is the mileage obtained at 90 mph?

Learn how to estimate the maximum and minimum gasoline mileage based on a speed vs. fuel economy graph. This problem covers graph interpretation, optimization of fuel economy, and properties of parabolas, suitable for students in Grades 9-12.

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