The temperature outside your home or school usually fluctuates throughout the day and night. In this project, you will record samples from the daily temperature and discuss various aspects of your data.
You will need a Calculator Based Laboratory (CBL), with temperature probe and your TI-83 Plus calculator. First, load the DAYTEMP program from the Prentice Hall companion Web site. Next, connect the TI-83 Plus calculator to the CBL that has a temperature probe in Chan 1. The program is designed to record the temperature every hour for 24 hours. It will store in the TI-83 Plus the number of hours, x, after you start the program for L3 and the temperature, y, in degrees Celsius for L4. The program will also graph the results on your calculator. Record the time that you start the program. Allow the program to run for a 24-hour period outside.
If you do not have time or equipment to collect the hourly temperatures, you may choose to use the projected hourly temperatures. A sample set of data points may also be found on the companion Web site.
Part I
Use the data collected to complete the exercises that follow. Let x be the number of hours after data collection began. Let y be the temperature in degrees Celsius.
1. Write ordered pairs for the set of data collected.
2. Use the data collected to sketch a graph of the daily temperatures. Label all points and the axes.
3. Determine the sets of numbers for the domain
and range of this relation. Explain the meaning of these sets
of numbers.
4. Does your data represent a function?
5. Does the graph have an x-intercept? If so, explain its meaning. If not, explain why not?
6. Does the graph have a y-intercept? If so, explain its meaning. If not, explain why not?
7. a. Determine any relative
minima. Where do they occur? Convert each relative minimun to time
of day and explain its meaning.
b. Determine
the absolute minimum - the lowest temperature of the day. Is this value
also a relative
minimum? For what x-value does it occur? Convert the absolute minimum
to time of day.
c. Determine
any relative maxima. Where do they occur? Convert each relative maximum
to time of day
and explain its meaning.
d. Determine
the absolute maximum - the highest temperature of the day. Is this value
also a relative
maximum? For what x-value does it occur? Convert the absolute maximum
to time of day.
8. Between what x-values is the temperature
increasing? Between what x-values is it decreasing? Convert the
x-values to time of day
and explain their meaning.
Part II
Now convert the temperature to Fahrenheit (to two decimal places), and repeat the previous set of exercises with your new data. Let x be the number of hours after data collection began. Let y be the temperture in degrees Fehrenheit.
1. Write ordered pairs for the set of data collected.
2. Use the data collected to sketch a graph of the daily temperatures. Label all points and the axes.
3. Determine the sets of numbers for the domain
and range of this relation. Explain the meaning of these sets
of numbers.
4. Does your data represent a function?
5. Does the graph have an x-intercept? If so, explain its meaning. If not, explain why not?
6. Does the graph have a y-intercept? If so, explain its meaning. If not, explain why not?
7. a. Determine any
relative minima. Where do they occur? Convert each relative minimum to
time of day
and explain its meaning.
b. Determine
the absolute minimum - the lowest temperature of the day. Is this value
also a relative
minimum? For what x-value does it occur? Convert the absolute minimum
to time of day.
c. Determine
any relative maxima. Where do they occur? Convert each relative maximum
to time of day
and explain its meaning.
d. Determine
the absolute maximum - the highest temperature of the day. Is this value
also a relative
maximum? For what x-value does it occur? Convert the absolute maximum
to time of day.
8. Between what x-values is the temperature increasing? Between what x-values is it decreasing? Convert the x-values to time of day and explain their meaning.