course MTH 271 09/08, 1600 dӠrp|vvvv
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20:19:40 `qNote that there are four questions in this assignment. `q001. Recall the stock value problem, where March, July and December values were $5000, $5300 and $5500. Construct a graph of stock value vs. number of month (e.g., 1 for Jan, 2 for Feb, etc.). You will have three points on your graph, one corresponding to the March value, one to the July value, and one to the December value. Stock value will be on the y axis and month number on the x axis. Your first point, for example, will be (3, 5000), corresponding to $5000 in March. Connect your three points with straight lines--i.e., connect the first point to the second and the second to the third. What is the slope of your line between the first and second point, and what is the slope of your line between the second in the third point? Recall that slope is rise / run.
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RESPONSE --> Slope between first point (3,5000) and second point (7,5300): (5300-5000)/(7-3)= 300/4 = 75 Slope between second point (7,5300) and third point (12, 5500): (5500-5300)/(12-7)= 200/5 = 40 confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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20:22:33 `q002. Look at your results for the slopes, and look the results for the average rates of change. What do you notice? In what way then does the graph represent the average rate of change?
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RESPONSE --> The slope and the average rates of change are equal. The graph represents the average rate of change by displaying the increase in stock value as the months pass. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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20:26:20 `q003. To what extent do you think your graph, consisting of 3 points with straight line segments between them, accurately depicts the detailed behavior of the stocks over the 9-month period?
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RESPONSE --> The straight line segments between the points are an approximation of the change in stock value during the time period. The exact value of the stock is given for months 3, 7, and 12. We do not, however, have values for the months in between. The lines between indicate the average change but, the actual value of the stock for each month may be above or below the average, and graphically, lie above or below the line. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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20:30:59 `q004. From the given information, do you think you can accurately infer the detailed behavior of the stock values over the nine-month period?
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RESPONSE --> From the given information, I believe we can infer the trend of the stock values over the nine-month period. But, with respect to individual months our inference may be incorrect. For instance, the stock value increased $300 dollars between months 3 and 7. This creates an upward sloping line in between the two values. This line indicates the average rate of change, but may or may not accurately represent the change for a particular month. If there were monumental increases in month 4 and/or a decrease in month 5, the points corresponding to the activity in these months would not fall on our line. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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ȳնƾ毹٧_w\ҽF assignment #003 003. 09-07-2009
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20:50:12 `qNote that there are four questions in this assignment. `q001. Sketch a graph similar to that you constructed for the stock values, this time for the depth of the water vs. clock time (depths 80, 40, 20 at clock times 10, 40, 90). Your first point, for example, will be (10, 80). Connect these points with straight lines and determine the slopes of the lines.
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RESPONSE --> Slope between point one (10,80) and point two (40,40): (80-40)/(10-40)=(40)/(-30)=4/-3 Slope between point two (40,40) and point three (20,90): (90-40)/(20-40)=(50)/(-20)=5/-2 confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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20:52:00 `q002. Look at your results for the slopes, and look the results for the average rates of change. What do you notice? In what way then does the graph represent the average rate of change?
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RESPONSE --> The slopes are negative in this equation. Therefore, the rate of change is negative, i.e., there is a decrease of water depth over time. confidence rating: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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20:58:38 `q003. To what extent do you think your graph with three points and straight line segments between them accurately depicts the detailed behavior of the water over the 80-second period of observation? How do you think the actual behavior of the system differs from that of the graph? How do you think the graph of the actual behavior of the system would differ from that of the graph you made?
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RESPONSE --> The graph best demonstrates the trend of the action taking place within the system. The water depth is decreasing over time. The lines between the points give the average rate of change during those periods. The actual depth may be decreasing at a rate faster/slower than the average. This difference would be observed if watching the behavior of the system. We would notice the depth of the water decreasing most quickly at first before slowing. Graphing this, if using only three points as with the given graph, the overall trend of both graphs would appear the same. confidence rating: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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21:03:04 `q004. From the given information, do you think you can accurately infer the detailed behavior of the water depth over the 80-second period? Do you think you can infer the detailed behavior better than you could the values of the stocks? Why or why not?
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RESPONSE --> I believe the behavior of the water could be reasonably inferred from the given information. The graph shows the decreasing depth of water changes at decreasing rate over time. If more accurate measurements were provided for each time interval, it is likely that the points would fall on or near the lines of our graph. The detailed behavior of the decreasing water is more easily inferred than that of stock values because of the unpredictable nature of stock values. We can approximate the water loss because we can predict the behavior of the water. We cannot, however, predict the behavior of the value increase/decrease of stocks. confidence rating: 2 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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