Title: Approximating Instantaneous Rates of Change Post-Video Questions
Course: Calculus Videos Project > Section: Approximating Instantaneous Rate of Change

Q: After filling up an 18-gallon gas tank, a SUV immediately starts to drive up a hill. While it is driving up the hill the SUV monitors its fuel consumption and the distance it has traveled since filling up its gas tank. The hill is becoming steeper and steeper and so the fuel economy measured in miles per gallon is decreasing. The SUV’s internal computer periodically records the amount of fuel consumed and its distanced traveled since filling up its gas tank, shown in the table below:

Fuel Consumed (gallons) | Distance Traveled (miles)
0.1 | 2.4
0.2 | 4.7
0.3 | 6.9
0.4 | 8.9
0.5 | 10.6
0.6 | 11.9
0.7 | 12.8
0.8 | 13.3

Using only the data from the table, what method could you use to find the best possible underestimate to the SUV’s fuel economy when it has consumed 0.5 gallons?  Note: Fuel economy is a positive value indicating the number of miles per gallon a vehicle is consuming.
- miles per gallon
- miles per gallon
- miles per gallon
- miles per gallon
- miles per gallon
- miles per gallon
- Take the average of b. and c.
A: miles per gallon

Q: After filling up an 18-gallon gas tank, a SUV immediately starts to drive up a hill. While it is driving up the hill the SUV monitors its fuel consumption and the distance it has traveled since filling up its gas tank. The hill is becoming steeper and steeper and so the fuel economy measured in miles per gallon is decreasing. The SUV’s internal computer periodically records the amount of fuel consumed and its distanced traveled since filling up its gas tank, shown in the table below:

Fuel Consumed (gallons) | Distance Traveled (miles)
0.1 | 2.4
0.2 | 4.7
0.3 | 6.9
0.4 | 8.9
0.5 | 10.6
0.6 | 11.9
0.7 | 12.8
0.8 | 13.3

Which statement below best explains why the value you found underestimates the SUV’s fuel economy (measured in miles per gallon) at 0.5 gallons?
- Because I used an amount of gallons less than 0.5 gallons.
- Because I used an amount of gallons greater than 0.5 gallons.
- Because I used an interval of gallons consumed that includes 0.5 gallons.
- Because the value I got for miles per gallon would be less than all other values for miles per gallon.
- Because the fuel economy measured in miles per gallon is decreasing, an average rate over an interval of gallons prior to 0.5 gallons must be an underestimate.
- Because the fuel economy measured in miles per gallon is decreasing, an average rate over an interval of gallons after 0.5 gallons must be an underestimate.
A: Because the fuel economy measured in miles per gallon is decreasing, an average rate over an interval of gallons after 0.5 gallons must be an underestimate.

Q: After filling up an 18-gallon gas tank, a SUV immediately starts to drive up a hill. While it is driving up the hill the SUV monitors its fuel consumption and the distance it has traveled since filling up its gas tank. The hill is becoming steeper and steeper and so the fuel economy measured in miles per gallon is decreasing. The SUV’s internal computer periodically records the amount of fuel consumed and its distanced traveled since filling up its gas tank, shown in the table below:

Fuel Consumed (gallons) | Distance Traveled (miles)
0.1 | 2.4
0.2 | 4.7
0.3 | 6.9
0.4 | 8.9
0.5 | 10.6
0.6 | 11.9
0.7 | 12.8
0.8 | 13.3

What additional information might you need to improve your underestimate to the SUV’s fuel economy (measured in miles per gallon) at the 0.5-gallon mark?
- I do not need to make an improvement because the rate I calculated is the SUV’s fuel economy at the 0.5-gallon mark.
- Use a different pair of points from the table to underestimate the rate.
- Use two pairs of points from the table to compute two rates, then average these rates.
- Use a larger interval of gallons (e.g., if I originally used a 0.1-gallon interval, a 0.2-gallon interval would improve my approximation).
- Use a smaller gallon interval (which might require additional data).
A: Use a smaller gallon interval (which might require additional data).