course Mth 271 ?w??????I??????W?assignment #002002.
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12:48:06 `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 --> Because slope is rise over run, we take the change in rise (stock value) and divide by the change in run (month value) 1st and 2nd points. 5300-5000/7-3 300/4 75 The slope of the first 2 points is 75. 2nd and 3rd points. 5400-5300/12-7 100/5 20 The slope of the second 2 points is 20. confidence assessment: 2
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12:49:10 The three points on the graph are (3, 5000), (7, 5300) and (12, 5500). The rise between the first point and the second is from 5000 to 5300, or 300, and the run is from 3 to 7, or 4, so the slope is 300 / 4 = 75. Note that the 300 represents $300 and the 4 represents 4 months, so the slope represents $300 / (4 months) = $75 / month, which is the average rate of change during the first time interval. The rise between the second point and the third is from 5300 to 5500, or 200, and the run from 7 to 12 is 5, so the slope is 200 / 5 = 40. This slope represents the $40/month average rate of change during the second time interval. Click on 'Next Picture' to see the graph.
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RESPONSE --> I forgot to include that the slope was represtented in $/month. But I do see and understand the statement. self critique assessment: 2
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12:50:36 `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 --> I notice that the average rate of change is decreasing. The first 2 points span 4 months with an average change of $75, where that second set on changes an average of $20 in 5 months. Less money in a longer period of time. confidence assessment: 2
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12:51:18 We see from this example that the slope of a graph of value vs. clock time represents the rate at which value is changing with respect to clock time.
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RESPONSE --> Ok. I understand what the question was asking now. I see that the slope represents the rate value is changing with respect to time. self critique assessment: 2
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12:52:55 `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 --> It represents a fairly accurate depiction of the behavior of stock over 9 months. This is because in 9 months, we only have 3 values. There are still 6 months that we are unable to see the behavior of the stocks. However, to obtain an even more accurate depiction, we should have all stock values of these 9 months. confidence assessment: 2
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12:53:50 Stocks can do just about anything from day to day-they can go up or down more in a single day than their net change in a month or even a year. So based on the values several months apart we can't say anything about what happens from day to day or even from month to month. We can only say that on the average, from one time to another, the stocks changed at a certain rate.
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RESPONSE --> This is much better explanation. I see now that stocks change day to day, or even minute to minute. So it is simply impossible for us to say what happens to these stocks every day. self critique assessment: 2
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12:54:42 `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 --> No. I don't believe it is possible. Like the previous question, stocks change daily, sometimes by the minute. So from 3 monthly values, it would be near impossible for me to give any detailed behavior of the stocks. confidence assessment: 2
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12:54:48 Not on a day-to-day basis, and not even on a month-to-month basis. All we can see from the given information is what might be an average trend.
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RESPONSE --> self critique assessment: 3
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