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course Mth 163
1. If you have not already done so, obtain your own set of flow depth vs. time data as instructed in the Flow Experiment (either perform the experiment, as recommended, or
click on Randomized Problems and select Precalculus then Simulated Data for Flow
Experiment , which can be accessed at http://164.106.222.236/interactivepro).
Complete the modeling process for your own flow depth vs. time data.
Use your model to predict depth when clock time is 46 seconds, and the clock time
when the water depth first reaches 14 centimeters.
Answer:14.92 cm
Answer: 47.78 sec
Comment on whether the model fits the data well or not.
Answer:It does.
Even though you probably understand the process at this point, it can be challenging
to get through these problems without making mistakes. An error on one step can
throw the entire problem off, and result in a model that doesn't work at all.
There is a limit to how much time you should spend worrying about finding and
correcting arithmetic mistakes. Of course it is important that you follow the solution
procedures correctly, that you recognize when your model doesn't work, and that you
do spend significant time trying to track down arithmetic errors. However if you
believe you are doing the procedures correctly (other than a pesky arithmetic error or
two), and have spent more than a couple of hours trying to track the error down, you
should proceed to the Query and submit your responses through Exercise 1. Wait for
your work to be posted before moving on to Exercise 2 below.
2. Follow the complete modeling procedure for the two data sets below, using a
quadratic model for each. Note that your results might not be as good as with the flow
model. It is even possible that at least one of these data sets cannot be fit by a
quadratic model.
Data Set 1
In a study of precalculus students, average grades were compared with the percent of
classes in which the students took and reviewed class notes. The results were as
follows:
Percent of Assignments Reviewed
Grade Average
0
1
10
1.790569
20
2.118034
30
2.369306
40
2.581139
50
2.767767
60
2.936492
70
3.09165
80
3.236068
90
3.371708
100
3.5
MY MODEL= -1.317x^2+0.033x+1.475=y
It's best to obtain and use your own model. However if after reasonable effort (an
hour or so) you fail to get a model that appears to make sense, you may use the model
y = - 0.0003·x^2 + 0.041·x + 1.41 to answer the questions below. When you do the
Query, you will be expected to show the work you have done up to this point. You
should then indicate that your model doesn't seem to work, and state that you are
using the y = - 0.0003·x^2 + 0.041·x + 1.41 model. This model isn't based on a very
good selection of points, so it's possible to get a much better model, but this one will
suffice to answer the questions.
Quadratic equations can't always be solved, so it is possible that some of the
questions asked below will have no answer.
Determine from your model the percent of classes reviewed to achieve grades of 3.0
and 4.0.
Answer:No Solution
Determine also the projected grade for someone who reviews notes for 80% of the
classes.
Answer:No Solution
Comment on how well the model fits the data. The model may fit or it may not.
Answer: Does not fit
Comment on whether or not the actual curve would look like the one you obtained, for
a real class of real students.
No. I kept getting negitive numbers at a decreasing rate. Therefore, it does
not seem to fit a class of real students.
Data Set 2
The following data represent the illumination of a comet by the sun at various
distances from the sun:
Distance from Sun (AU)
Illumination of Comet (W/m^2)
1
935.1395
2
264.4411
3
105.1209
4
61.01488
5
43.06238
6
25.91537
7
19.92772
8
16.27232
9
11.28082
10
9.484465
Obtain a model.
MY MODEL:24.034x^2-367.22x+1278.327=y
It's best to obtain and use your own model. However if after reasonable effort (an
hour or so) you fail to get a model that appears to make sense, you may use the model
256·x^2 - 1439·x + 2118 to answer the questions below. When you do the Query, you
will be expected to show the work you have done up to this point. You should then
indicate that your model doesn't seem to work, and state that you are using the y =
256·x^2 - 1439·x + 2118 model. This model isn't based on a very good selection of
points, so it's possible to get a much better model, but this one will suffice to answer
the questions.
Quadratic equations can't always be solved, so it is possible that some of the
questions asked below will have no answer.
Determine from your model what illumination would be expected at 1.6 Earth
distances from the sun.
Answer:y=752.30204
At what range of distances from the sun would the illumination be comfortable for
reading, if reading comfort occurs in the range from 25 to 100 Watts per square meter?
Answer:5.168
Analyze how well your model fits the data and give your conclusion. The model might
fit, and it might not. You determine whether it does or doesn't.
Answer:It fits pretty good"
You have submitted only answers to the questions, with no documentation. You need to document how you obtained your answers.
You can resubmit a copy of this document, showing how you got your results.
Alternatively, it will probably be easier for you to submit the Open Query for this assignment, which asks specific questions adn which will save you a lot of typing.
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