Lab 11:

Linear functions

Part I:

Linear models can be created for real world settings.  For each of these  described setting, give a formula for the corresponding linear model and use the formula to answer the question. 

a.  A calling card offers a price of $0.23 cents per minute at any time during the day with a monthly service charge of $1.00.  Express the monthly cost as a function of minutes called. 

How much will it cost to talk 400 minutes in a month?

b. At 0 degrees Celsius, the speed of sound is 350 meters per second and it increases by 0.2 m/s for each increase of 1 degree Celsius.  Express the speed of sound as a function of temperature in Celsius.

What will be the speed of sound at 37 degrees? 

Part II:

2.    Open the file CarsAndTrucks_By_Year1970-MostRecent.xls contains data from the Bureau of Labor Statistics number of cars and small trucks on the road from 1970 through 2007.

a.     Make an X-Y scatter plot of the data including the trendline and the regression equation.  Make sure that the years are the X values.  Note that Excel will, in most cases, put a legend on your graph by default.  When there is only one data series (as here), you don't need a legend, and it really should be removed.  Paste this chart in your Word document. 

b.    Write a brief statement in your own words stating what the linear function shows about the historical trend in the number of vehicles.  Make your statement as precise as possible, meaning that you use the numbers included in the linear function (regression equation). 

3.    Open the file Coal_Consumption2004.xls containing data from the U.S. Energy Administration.  The unit of measure here is quads, a standard measure standing for quadrillion BTU's. (A British Thermal Unit is a unit of energy, the amount of energy needed to raise 1 pound of water 1 degree Fahrenheit when the water is about 39.2 degrees Fahrenheit.)

a.     Make an X-Y scatterplot of the data. Add a trendline, including the equation of the line.  Paste this chart into your Word document.

b.    Write a brief statement in your own words stating what the linear function shows about the historical trend in the number of vehicles.  Make your statement as precise as possible, meaning that you use the numbers included in the linear function (regression equation).