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/statisticalabstractus.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.
 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?
 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
 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).
 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.
 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.