#$&*
course Mth163
6/7 10
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
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.
I obtained a quadratic equation using data points (10, 1.790569), (40, 2.581139), (70, 3.09165)
y = -.0001556(x^2) + .034(x) + 1.467
Determine from your model the percent of classes reviewed to achieve grades of 3.0 and 4.0.
My model predicted using the quadratic formula the percent of the class that would that achieve grades of 3.0 would be 87.484, which doesn't make sense. I couldn't come up with an answer 4.0 grades.
@&
That does make sense. 87% review achieves a grade of 3.0.
It is also possible that it's a tough course and a 4.0 is not possible.
Your model gives results consistent with those obtained by most students who do the problem correctly.
*@
Determine also the projected grade for someone who reviews notes for 80% of the classes.
My predicted grade for someone that reviewed 80% of the the notes is 3.19116
Comment on how well the model fits the data. The model may fit or it may not.
The model didn't fit very well, but seemed reasonable for some. I observed a deviation of 0.007606
Comment on whether or not the actual curve would look like the one you obtained, for a real class of real students.
I think it's reasonable, because just reviewing assignments wouldn't guarantee a 4.0.
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.
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.
I obtained a quadratic equation y = 65.619(x^2) - 677.484(x) + 1547.005 using points (1, 935.1395), (3, 105.1209), and (7, 19.92772)
Determine from your model what illumination would be expected at 1.6 Earth distances from the sun.
631.01524 W/m^2
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?
can't answer this question
@&
You should specify why you can't answer the question.
However if you replace the illumination by 25 and solve the resulting quadratic you get a distance corresponding to that illumination.
Doing the same for illumination 100 you do get a range of distances.
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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.
The model doesn't fit well at all.
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&#This looks good. See my notes. Let me know if you have any questions. &#