Number of Vehicles

Acquisition

The table below lists the number of passenger vehicles in the United States for selected years. This 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
Number Registered (millions) 161 177 193 198 210

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 the number of registered vehicles is increasing per year?

Application

Next you 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.

Number of Vehicles

  1. Create a linear model. For this question, use the linear regression applet.
    a) Plot the data on from the (t, V) coordinate system where t = 0 in 2000 and V is the number of passenger vehicles (in millions).
    b) Use linear regression to derive the function which describes the number of vehicles (in millions) in year 2000+t. Call this function V (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 vehicles in the US in 2005.
    b) Predict when the number of vehicles will reach 300 million.
  4. Be sure to save your function to use for the rest of the module.