## Transcribed Text

A small gold-rush era town called Golden had the following census data. Let 1860 be time zero for this problem and assume the
populations are for January 1 of that year. (The "x-axis" must represent time.)
Calendar Year (January 1st)
1/1/1860
1/1/1870
1/1/1880
1/1/1890
P(t) Population (number of people)
1260
1010
885
625
1. Determine a linear equation (use LinReg) for the given data. P(t) =
2. What is the meaning of the slope ?
3. Determine Golden's population for January 1st of the year 1896.
(round to a whole number)
4. During what year (i.g. during the year of 1902 ) will Golden become a "ghost town "?
Version 030405 MATH 123 ACTIVITY: THE DENSITY OF GLASS USING LINEAR REGRESSION
ROW
4
SEAT# 4
CLASS PERIOD
8
NAME Asman
In this activity you and your partner(s) will create a data table (and then a scatter plot) for the mass and volume of numerous pieces
of glass. It is unlikely that the data you obtain will be "perfectly" linear. However, the data should be "almost" perfectly linear if
your
measurements and calculations are correct. Your instructor will give you the necessary equipment including 50 pieces of glass.
You will assume that each piece of glass is identical and has an average mass of 3.68 grams per piece. Since glass is heaver than
water the glass pieces, when added to the container, will force the water level to rise This method of finding the density of an
object(s) is called the WATER DISPLACEMENT METHOD.
1. Place 8 pieces of glass into the plastic container. Read the volume to the nearest whole cubic centimeter (cm³). Record the data
in the data table. Calculate the mass of the 8 pieces of glass and enter the value in the data table. Keep one decimal place.
2. Divide the remaining pieces of glass into four somewhat unequal piles. For example 12, 9, 11, and 10.
3. Repeat step 1 above for the remaining piles. The Volume reading and the Total Mass columns will get larger each time your add
more piece of glass to the container. Eventually you will plot the Total Mass on the y-axis and the Volume reading on the x-axis.
SCATTER PLOT: MASS (g) vs. VOLUME (cm³
# added
Total
Volume
Total
per set
#
Reading
Mass
(cm³)
(g)
8
8
IRO
29.44
10
18
130
66.24
250
1
25
143
92
2
37
159
136.16
4
41
165
150.8
200
4. (a) Make an accurate scatter plot
on the graph paper at the right.
(b) Hand draw a line that you think
150
"best fits" the data points. Be sure to
extend the line to cross the
Volume axis.
100
50
*** OVER ***
50
100
150
200
250
Volune C Cm
3)
5. Using your calculator, make the same scatter plot in your calculator and then find the "best fit" line, using your TI-83, that would
pass through (or almost through) your five data points. Round your a and b values keeping two decimal places.
Let the mass, M(V) be a function of the volume, V. The regression Equation, in functional notation, is
:
M(V) =
6. The slope in the regression equation ( a = = will have the label of the y-axis divided by the label of the x-axis. What
will the label(s) be for the slope of your line?
The label(s) for the slope will be:
The numerical value of your slope plus the labels from #6 will be the density of the glass. !. If the Activity goes well your density
value for the glass pieces should be about 2.55 g/cm³.
7. The point where your line crosses the x-axis is called a "zero". What are the coordinates of your zero? (
,
)
8. How do the coordinate values of the "zero" relate (have a meaning) to this activity? Explain your answer.
9. If the volume reading was 305 cm³, , how many grams of glass should be in the container?
Mass =
grams
10.
Your partner informs you that there are 136.53 grams of glass in the container. If 1 piece of glass = 3.69 grams, how many
pieces of glass must be in the container?
Number of pieces of glass =
pieces
11. Suppose you added an additional 30 pieces of glass to the container, and some of the glass pieces were not completely covered by
the water. If this information was add to your data table would the Volume reading be wrong or would the Total Mass value be
wrong?
The
entry would be wrong.
12. Suppose you have a beautiful antique egg-shaped glass paperweight. You place it in a container of water (the water
displacement
method) and determine that the glass paper weight displaces 172 cm³ of water Hence you know that the volume of the
glass paper weight is 172 cm³. What is the mass of the antique glass paper weight? HINT : use the DENSITY of glass
As A FACTOR,

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction
of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice.
Unethical use is strictly forbidden.