open qa 1

#$&*

course Mth 173

1/16 2:32 p.m.

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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:

not sure if it wants that based on certain months have more days than others, so im just going of the thought of period is ""mid""

so its equal distance from a mid to a mid. march april may june july, 4 months past with a 300 dollar increase. july august sept

oct nov dec. or a 200 dollar increase in 5 months. even if the days where counted, the 4 monthgs for 300 should be more.

confidence rating #$&*: 3

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Given Solution:

`aThe 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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Self-critique (if necessary):OK

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Self-critique Rating:OK

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

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Your solution:

change per what? per day, the average with the two periods together?

@&
Two periods are given in the data, so you would find an average rate for each.

Since the periods are in months the easiest way to calculate would be per month. However months have differing numbers of days, so you could certainly calculate the result in days, or in any other unit of time.
*@

I will assume the two periods together, and

4months/300 and 3months/200 7months/500 divide by 2 = * 1/2 so (7/500) * (1/2) 7/1000 the average is $1000.00 per 7

months, or if you want that by month, 7/1000 = 1/x 7x= 1000. x= 142.86 rounded.

so every 7 months $1000

or per month $142.86 rounded

confidence rating #$&*:2

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Given Solution:

`aFrom 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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Self-critique (if necessary):

I did not properly understand the question. It wanted me to find the reate per month of both ranges. This is to check and

make sure that since one was by 4 months, and other by 5, that wasnt the reason why one was larger than the other.

@&
As you would have seen in the Rates exercise of the Initial Activities, and elsewhere, an average rate is the change in one quantity divided by the change in another.

Both changes are needed to determine an average rate, and both would affect which rate is greater.
*@

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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:

at 10 seconds 80

at 40 seconds 40 (30 seconds have past, water decreased 40cm)

at 90 seconds 20 (50 seconds have past, water decreased 20cm)

the time lapse has increased, and even with the time lapse being larger, the decrease was smaller than previous, so the depth of

the water is changing less quickly. This means the earlier it is, the faster, so between the first two it is fast, last two it is slow.

Reasoning probably with the pressure being less because not as much water pushing down. This also reminds me of hydraulics.

confidence rating #$&*: 3

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Given Solution:

`aBetween clock times t = 10 sec and t = 40 sec the depth changes by -40 cm, from 80 cm to 40 cm, in 30 seconds. The

average rate is therefore -40 cm / (30 sec) = -1.33 cm/s.

Between t = 40 sec and t = 90 sec the change is -20 cm and the time interval is 50 sec so the average rate of change is -20

cm/ 50 sec = -.4 cm/s, approx.

The depth is changing more quickly during the first time interval.

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Self-critique (if necessary): OK

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Self-critique Rating: OK

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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:

it is a time lapse with a changing value. one just has to deal more with money and investment, the other to do more with in my

mind i want to say science, and just a law of gravity, along with pressure etc. It is mathematically the same, as you can set it up

almost the same way.

by how much time has past, over the amount of change, to compare values

confidence rating #$&*: 2

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Given Solution:

`aIn 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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Self-critique (if necessary):

if d stands for delta, then I understand this.

@&
`d is a two-character symbol that stands for Delta. Both the backward apostrophe and the d are necessary.

d by itself has another interpretation related to, but not the same as that of `d.

*@

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Self-critique Rating: OK.

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:

To have a real word context to base what we should know. It is to review in case our knowledge is inadequate (which I

believe mine was, my teacher was to worried about the SOL's so I didn't feel like I gained much from the course, to my

displeasure).

@&
That's not necessarily your teacher's fault. The SOL is a very bad test, but it's been imposed on teachers throughout Virginia in a way that has unfortunate results.
*@

confidence rating #$&*: 2

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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 found it by clicking the brief assignments page, in assignments 01 row.

confidence rating #$&*: 3

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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 assume, from being expected that we are to do these modeling projects, that they will be easy materials, and not be messy, or

a hassle (with the assumption of the expirement being performed correctly). That there is also an open query following these

experiments that asks question about the work done, as well as other things.

@&
Whether they are easy or not depends largely on your background. If you've had a decent analysis or precalculus course they should be pretty easy. If not, they provide a necessary supplement.
*@

@&
They do take a significant amount of time, but that is to be expected in a college-level course.
*@

confidence rating #$&*: 3"

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Self-critique (if necessary):

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