Average Mileage

Acquisition

The table below lists the average number of miles that a passenger vehicle travels per year. 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 Vehicle (thousands) 9.5 10.0 11.1 11.6 11.8

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. On the average, how much do you think the number of miles a car is driven changes in a 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.

Average Miles Driven per Year

  1. Create a linear model. For this question, use the linear regression applet.
    a) Plot the data on a (t, M) coordinate system where t = 0 in 2000 and M is the average number of miles a passenger vehicle is driven (in thousands).
    b) Use linear regression to derive the function which describes the average miles driven per vehicle (in thousands) in year 2000+t. Call this function M(t).
  2. Interpret the function.
    a) Give a verbal interpretation of the slope.
    b) Give a verbal interpretation of the y-intercept.
  3. Use the function
    a) Predict the number of miles an average passenger vehicle will be driven in 2005.
    b) Predict when the average vehicle will be driven 15,000 miles per year.

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