Real-Life Applications of Functions and Graphs : Heart Disease / Cancer and Fahrenheit / Celsius Temperature Conversions

You have been invited to present statistical information at a conference. To prepare, you must perform the following tasks:

1.The following data was retrieved from www.cdc.gov. It represents the number of deaths in the United States due to heart Disease and cancer in each of the years; 1985, 1990, 1995, and 2002.

  Year
Disease         1985        1990      1995      2002
Heart Disease   771169     720058    737563     696,947
Cancer      461563       505322    538445     557,271

2.
a. Plot this data for each disease as points in a rectangular coordinate  system.
b. Using a smooth line, connect your data points for each disease.
c. On a separate graph, plot only the years 1985 and 2002 and connect the points with a straight line.
d. Calculate the slope of each line.
e. Write the equation of each line in the slope-intercept form.
f. Using the equations of each line, make a reasonable prediction as to the number of deaths we might expect in 2005 due to each of these medical conditions.


2.
a.    Can the graphs that you constructed be classified as functions? Explain.
b.    Why is it reasonable that negative numbers are excluded from both the domain and the range of each of the disease graphs? What would the real-world implications be if these numbers were actually part of the domain and/or range?


3.

1.  In the real world, what might be a situation where it is preferable for the data to form a relation but not a function?
2.  There is a formula that converts temperature in degrees Celsius to temperature  in degrees Fahrenheit. You are given the following data points:

                                 Fahrenheit   Celsius
            Freezing point of water   32     0
            Boiling point of water   212    100

1. Find the linear equation that expresses temperature in degrees Fahrenheit as a function of temperature in degrees Celsius.
2. Find the linear equation that expresses temperature in degrees Celsius as a function of temperature in degrees Fahrenheit.
3. How do the graphs of these two functions differ?