below lists the average number of miles that a passenger vehicle
travels per year. The information is from the Bureau of Transportation
For additional information, see Statistical Abstracts of the US
Census Bureau, (http://www.census.gov/prod/www/statistical-abstract-us.html).
Miles Traveled per Vehicle (thousands)
questions below to your journal and record the answers there.
- What trends
do you observe from these data?
- Do you
think these trends will continue in the near future?
- What kinds
of functions (linear, quadratic, exponential, etc.) would accurately
describe the trends over the last twentyfive years?
- On the
average, how much do you think the number of miles a car is
driven changes in a year?
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.
Miles Driven per Year
a linear model. For this question, use the linear
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).
a) Give a verbal interpretation of the slope.
b) Give a verbal interpretation of the y-intercept.
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
to save your function to use for the rest of the module.