below lists the number of passenger vehicles in the United States
for selected years. This 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).
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?
how much do you think the number of registered vehicles is increasing
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
a linear model. For this question, use the linear
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
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).
a) Give a verbal interpretation of the slope.
b) Give a verbal interpretation of the y-intercept.
a) Predict the number of vehicles in the US in 2005.
b) Predict when the number of vehicles will reach 300 million.
- Be sure
to save your function to use for the rest of the module.