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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,

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