q_a 1

course Mth 173

assignment #001001. Depth vs. Clock Time and Rate of Depth Change

Your work has been received. Please scroll through the document to see any inserted notes (inserted at the appropriate place in the document, in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

06-14-2007

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23:12:31

`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 -->

We see a greater rate of growth in the stocks during the first period, March-July.

confidence assessment: 2

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23:19:07

`q002. What were the precise average rates of change during these two periods?

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RESPONSE -->

There is an average rate of growth of $75 during the first period, and an average of $40 during the second month.

confidence assessment: 2

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23:29:20

`q003. If the water in a uniform cylinder is leaking from a hole in the bottom, and if the water depths at clock times t = 10, 40 and 90 seconds are respectively 80 cm, 40 cm and 20 cm, is the depth of the water changing more quickly or less quickly, on the average, between t = 10 sec and t = 40 sec, or between t = 40 sec and t = 90 sec?

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RESPONSE -->

The depth of the water changes more quickly during the first time interval (10-40 sec). This is because we see a drop of 40cm during the first period, rather than only 20cm in the second.

confidence assessment: 2

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23:37:07

`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 -->

In the two preceding problems, we reason out the largest of the two intervals. They are also directly linked to time.

confidence assessment: 1"

Good work. Let me know if you have questions.