You are about to erase your work on this activity. Are you sure you want to do this?

Updated Version Available

There is an updated version of this activity. If you update to the most recent version of this activity, then your current progress on this activity will be erased. Regardless, your record of completion will remain. How would you like to proceed?

Mathematical Expression Editor

Chat

Please answer each of these questions to the best of your ability. You are welcome to
re-watch parts of any of the videos to help you.

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.

(a) miles per gallon(b) miles per gallon(c) miles per gallon(d) miles per
gallon(e) miles per gallon(f) miles per gallonTake the average of (b) and (c)

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.

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).