Fuel Efficiency

Acquisition

The table below gives the average fuel efficiency for passenger vehicles for selected years. The information is from the Bureau of Transportation Statistics, http://www.bts.gov/btsprod/nts/. For additional information, see Statistical Abstracts of the US Census Bureau, (http://www.census.gov/prod/www/statistical-abstract-us.html).

  1980 1985 1990 1993 1996
Average Miles Traveled per Gallon 13.3 14.6 16.4 16.7 16.9

Copy the questions below to your journal and record the answers there.

    1. What trends do you observe from these data?
    2. Do you think these trends will continue in the near future?
    3. What kinds of functions (linear, quadratic, exponential, etc.) would accurately describe the trends over the last twentyfive years?
    4. Approximately how much do you think average fuel efficiency changes each year?

Application

Next you will apply relevant mathematical knowledge to analyze the trends you might have observed. You will construct a function to predict the total amount of gasoline burned by all passenger vehicles in a given year. Copy the questions to your journal and record your answers there.

Fuel Efficiency

  1. Create a quadratic model. For this question, use the Quadratic Regression quadratic regression applet.
    a) Plot the data on a (t, E) coordinate system where t = 0 in 2000 and E is the fuel efficiency in miles per gallon..
    b) Use quadratic regression to derive the function which describes the fuel efficiency in year 2000+t. Call this function E(t).
  2. Interpret the function.
    a) Graph E(t).
    b) The graph in a) is a parabola. Determine the coordinates of the vertex of the parabola.
    c) Give a verbal interpretation of vertex.
  3. Use the function
    a) Predict the fuel efficiency in the US in 2005.
    b) Predict when the fuel efficiency will begin to decrease. When will it fall to 1990 level?

Be sure to save your function to use for the rest of the module.