course Mth 271 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: `aThe 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. `routine graph2 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK Self-critique Rating: ********************************************* Question: `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? ********************************************* Your solution: The average rate of change is the change in y/ change in x. This scenario is similar to the depth vs time model. Confidence Assessment: 2
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Given Solution: `aWe 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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): OK Self-critique Rating: ********************************************* Question: `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? ********************************************* Your solution: The graph is quite accurate showing the first line segment having a steeper slope than the second. The difference in the two slopes is in both the stock value and the number of months. Between the first two points, the stock value changes by $300 over 4 months. Between the second and third points, the stock value changes by $200 over 5 months. Since we know the value of the stocks, we can accurately depict their behavior of these nine months however, we cannot break down the information any further than when it is given. Confidence Assessment: 3
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Given Solution: `aStocks 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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): Even though the stocks can change from day to day, we were told the values for these stocks over these nine months. Therefore we can accurately depict the behavior in these nine months based on the information that was given to us. Self-critique Rating: ********************************************* Question: `q004. From the given information, do you think you can accurately infer the detailed behavior of the stock values over the nine-month period? ********************************************* Your solution: We cannot break the information given down any further. We are only given between 4 months and 5 months. To break it down any further is guessing, not accuracy. Confidence Assessment: 3
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Given Solution: `aNot 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.