course Mth 173 íÌÓÄÚ×ÍÄîö†•²‡v©Äè‹ìyassignment #003
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21:44:19 `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 --> Point (10, 80) to (40, 40) slope: 40/30 = 1.33. Point (40, 40) to (90, 20) slope: 30/50 = 0.6. confidence assessment: 3
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21:44:35 The three points are (10, 80), (40, 40) and (90, 20). From the first point to the second the rise is from 80 to 40, or -40, and the run is from 10 to 40, or 30. So the slope is -40 / 30 = -1.33. From the second point to the third the rise is from 40 to 20, or -20, and the run is from 40 to 90, or 50, so the slope is -20 / 50 = -.4. Click on 'Next Picture' to see graph.
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RESPONSE --> Phooey. I forgot the negative signs. self critique assessment: 3
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21:45:43 `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 graph represents the average rate of change because the lines between the points are straight. It is very unlikely that the actual rate of change was actually the same as the average rate of change. confidence assessment: 2
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21:46:11 The slopes and the rates of change are numerically equal. For example between the second and third points the rise of -20 represents the -20 cm change in depth and the run of 50 represents the 50 seconds required to make this change, so the slope represents the -20 cm / (50 sec) average rate of change over the second time interval. We therefore see that slope represents average rate of change.
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RESPONSE --> Ah, slopes and rates are equal. Missed that. Close. self critique assessment: 3
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21:50:59 `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 only represents the average changes between these points, therefore it probably does not represent the actual behavior accurately. Probably the actual behavior of the system was initially changed faster and then finally changed slower during the interval. The actual behavior graph would be a much smoother curve rather than the straight lines between the points. confidence assessment: 2
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21:51:26 The straight line segments would indicate a constant rate of change of depth. It is fairly clear that as depth decreases, the rate of change of depth will decrease, so that the rate of change of depth will not be constant. The graph will therefore never be straight, but will be a curve which is decreasing at a decreasing rate.
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RESPONSE --> I think I got that. self critique assessment: 3
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21:54:37 `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 --> No, I cannot accurately infer the detailed behavior over the 80-second period because I don't have enough information to do so. With these three points I can only get an average idea of what is happening, not any specifics. I think we can infer the detailed behavior a little more than the stocks because if the water depth behaves in a somewhat uniform method, then the general idea of the behavior is probably closer to the actual behavior. confidence assessment: 2
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21:55:08 It will turn out that three data points will be sufficient to infer the detailed behavior, provided the data are accurate. However you might or might not be aware of that at this point, so you could draw either conclusion. However it should be clear that the behavior of the water depth is much more predictable than the behavior of the stock market. We don't know on a given day whether the market will go up or down, but we do know that if we shoot a hole in the bottom of a full bucket the water level will decrease, and we expect that identical holes in identical buckets should result in the same depth vs. clock time behavior.
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RESPONSE --> Okay. Interesting. self critique assessment: 3
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