title: Depth vs. Clock Time and Rate of Depth Change
001. Depth vs. Clock Time and Rate of Depth Change
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Question: `qNote that there are four questions in this assignment.
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Question: `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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Your solution:
My money was growing faster from March-July. We made $300 during a 4 month time period and only $200 over a 5 month period during July - December.
confidence rating #$&*
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Self-critique: OK
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Self-critique rating #$&* 3
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Question: `q002. What were the precise average rates of change during these two periods?
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Your solution:
Rate 1 = 300/4 = $75/month increase from March - July
Rate 2 = 200/5 = $40/month increase from July - December
confidence rating #$&*
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Self-critique: OK
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Self-critique rating #$&* 3
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Question: `q003. If the water in a uniform cylinder is leaking from a hole in the bottom, and if the water depths at clock times t = 10, 40 and 90 seconds are respectively 80 cm, 40 cm and 20 cm, is the depth of the water changing more quickly or less quickly, on the average, between t = 10 sec and t = 40 sec, or between t = 40 sec and t = 90 sec?
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Your solution:
t | Seconds
============
10 | 80 cm
40 | 40 cm
90 | 20 cm
============
Rate 1 = -40 cm / 30 sec = -1.33 cm/sec
Rate 2 = -20 cm / 50 sec = -0.4 cm/sec
The depth of the water is changing more quickly, on the average, between t = 10 sec and t = 40 sec due to the higer water change rate of -1.33 cm/sec.
confidence rating #$&*
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Self-critique: OK
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Self-critique rating #$&* 3
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Question: `q004. How are the two preceding questions actually different versions of the same question? How it is the mathematical reasoning the same in both cases?
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Your solution:
In order to solve both equations, you had to find 2 different rates based on certain given values and then compare them.
confidence rating #$&*
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Self-critique: OK
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Self-critique rating #$&* 3
The remainder of this initial q_a_ assignment concerns the Modeling Project assignments that are part of your course.
Question `q005: Different courses are taught with different goals and different emphasis, and no course covers everything. This is certainly true of your prerequisite precalculus (or equivalent) course. This doesn't mean that your precalculus or equivalent course was not a good course (from the preparation of students coming into these calculus courses it appears that some are excellent and some are inadequate, with most somewhere in between).
Part of your present calculus course consists of Modeling Project Assignments. These assignments include ideas and techniques related to quadratic, power and exponential functions, and the concept of proportionality. They are presented in a real-world context (which is not fairly common but not universal among good precalculus courses). Ideally you will have developed these skills in your prerequisite Precalculus or equivalent course. However different courses are taught to different standards, and students frequently enter this course without a good understanding of these functions, techniques, and concepts.
These topics are therefore part of your review of prerequisite material, which also includes the first chapter in your text. (You are very likely to find things in that chapter that you haven't covered in the prerequisite courses, which is of course why those chapters are there).
These Modeling Projects are assigned on your Assignments page, in the appropriate assignments.
Please summarize below your understanding of the reason for these modeling projects:
Your response:
I understand why the instructor is providing the review of these topic. I am a little confused on where to find the ""Modeling Projects"". I have completed Assignment 0 and working on Assignment 1 and have not seen any link to the ""Modeling Projects"".
If you search your Assingments page for the word 'modeling' you will find that modeling projects are assigned in Assts 2, 4, and 6, I believe. Just click on the links.
confidence rating #$&*
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Self-critique: OK
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Self-critique rating #$&* 3
Question `q006: The modeling projects are found by clicking on the obvious link on your assignments page, part of the title of which is 'Modeling Project # '. You are advised to look on your Assignments page to locate at least one such link, click on it and see that the link leads you to a worksheet or series of worksheets.
Please summarize below your understanding of how to access the modeling projects.
Your response:
I have searched the Assignments page and have found the Modeling projects now.
confidence rating #$&*
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Self-critique: OK
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Self-critique rating #$&* 3
Question `q007: The modeling projects include a number of exercises.
You are expected to do these exercises as you work through the Modeling Project. You are not expected to submit your work on the exercises, but you may certainly submit questions about them. The Open Query for the corresponding assignment will then ask selected questions about your work on the exercises in the Modeling Project, as well as other material that is part of the assignments.
Please summarize you understanding of the fact that there are exercises in the Modeling Projects, which you are expected to do, and which will appear in the Open Query for the corresponding assignments:
Your response:
I understand that I need to work on the Model project assignments and can submit any questions I have about them.
confidence rating #$&*
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Self-critique: OK
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Self-critique rating #$&* 3 "
&#This looks good. Let me know if you have any questions. &#
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