course Mth 271 ßüèÍÌ}â„”ñ†¾©tŠY³³Üƒassignment #001
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12:15:44 `qNote that there are four questions in this assignment. `q001. If your stocks are worth $5000 in mid-March, $5300 in mid-July and $5500 in mid-December, during which period, March-July or July-December was your money growing faster?
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RESPONSE --> 5300-5000/7-3= 300/4= $75 per month from March to July 5500-5300/12-7= 200/5= $40 per month July to Decemeber It is clear that from March to July the money was growing faster. confidence assessment: 2
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12:17:10 The first period (4 months) was shorter than the second (5 months), and the value changed by more during the shorter first period (increase of $300) than during the longer second perios (increase of $200). A greater increase in a shorter period implies a greater rate of change. So the rate was greater during the first period.
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RESPONSE --> self critique assessment: 0
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12:21:04 `q002. What were the precise average rates of change during these two periods?
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RESPONSE --> I believe the precise rates of change would be $75 per month during the first period and $40 per month during the second period. confidence assessment: 1
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12:22:19 From mid-March thru mid-July is 4 months. A change of $300 in four months gives an average rate of change of $300 / (4 months) = $75/month. From mid-July through mid-December is 5 months, during which the value changes by $200, giving an average rate of $200 / (5 months) = $40 / month. Thus the rate was greater during the first period than during the second.
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RESPONSE --> I understand where I miscalculated on the first question now. self critique assessment: 1
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12:27:42 `q004. How are the two preceding questions actually different versions of the same question? How it is the mathematical reasoning the same in both cases?
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RESPONSE --> I meant to answer the last problem that by saying that by graphing the solutions it show that from 40 to 80 it is going quicker than from 10 to 40. (I hit something on the keyboard and it skipped it before it would let me answer it.) The two preceeding questions are both dealing with depth and clock time. They would both be answered in the same way, only the first one is in dollars and the second one is in cm. confidence assessment: 2
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12:28:20 In each case we were given a quantity that changed with time. We were given the quantities at three different clock times and we were asked to compare the rates of change over the corresponding intervals. We did this by determining the changes in the quantities and the changes in the clock times, and for each interval dividing change in quantity by change in clock time. We could symbolize this process by representing the change in clock time by `dt and the change in the quantity by `dQ. The rate is thus rate = `dQ /`dt.
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RESPONSE --> self critique assessment: 0
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