jdf004

course mth271

For mth004When submitting your work electronically, show the details of your work and give a good verbal description of your graphs.

One very important goal of the course is to learn to communicate mathematical thinking and logical reasoning. If you can effectively communicate mathematics, you will be able to effectively communicate a wide range of important ideas, which is extremely valuable in your further education and in your career.

When writing out solutions, self-document. That is, write your solution so it can be read without reference by the reader to the problem statement. Use specific and descriptive statements like the following:

· Using the depth vs. clock time data points (0, 13), (3, 12), (10,10), (25,8), (35, 6), (52, 3), (81, 1), we obtain a model as follows . . .

· Using the depth vs. clock time data points (3, 12), (25, 8) and (52,3) we obtain the system of equations . . .

· From the parameters a = -1.3, b = 12 and c = 15 we obtain the function . . .

· Comparing the predicted depths at clock times t = 0, 3, 10, 25, 35, 52, 81 with the observed depths we see that . . .

Here are some data for the temperature of a hot potato vs. time:

Time (minutes) Temperature (Celsius)

0 111

8 111

16 91.08563

24 82.93105

32 75.78268

40 69.5164

48 64.02332

56 59.20807

Graph these data below, using an appropriate scale:

Pick three representative points and circle them.

Write the equations that result from the assumption that the appropriate mathematical model is a quadratic function y = a t^2 + b t + c.

Eliminate c from your equations to obtain two equations in a and b.

Solve for a and b.

Write the resulting model for temperature vs. time.

Make a table for this function:

Time (minutes) Model Function's Prediction of Temperature

0 109

8 99.234

16 89.468

24 79.7026

32 69.9368

40 60.1711

48 50.4053

56 40.6395

Sketch a smooth curve representing this function on your graph.

Expand your table to include the original temperatures and the deviations of the model function for each time:

Time (minutes) Temperature (Celsius) Prediction of Model Deviation of Observed Temperature from Model

0 111 109 -2

8 100.3881 99.234 -1.1541

16 91.08563 89.468 -1.61763

24 82.93105 79.7026 -3.22845

32 75.78268 69.9368 -5.84588

40 69.5164 60.1711 -9.3453

48 64.02332 50.4053 -13.61802

56 59.20807 40.6395 -18.56857

Find the average of the deviations. –6.92224

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 E-mail the instructor for a set of data).

Complete the modeling process for your own flow depth vs. time data.

My model is Y=(0.0043)t^2-.5835t+20

Use your model to predict depth when clock time is 46 seconds, and the clock time when the water depth first reaches 14 centimeters.

(46,2.2578) and (11,14)

Comment on whether the model fits the data well or not?

It seems to fit good with an average deviation of only 0.165

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 .7087566

10 1.122194

20 1.486884

30 1.808573

40 2.092333

50 2.342635

60 2.563424

70 2.75818

80 2.929973

90 3.08151

100 3.215179

**Y=-0.00015t^2+0.39511t+0.74052**

Determine from your model the percent of classes reviewed to achieve grades of 3.0 and 4.0. for 3.0 (85,3.0) for 4.0 I got an imaginary number

Determine also the projected grade for someone who reviews notes for 80% of the classes. For this person according to the model would get 2.9414 grade average

Comment on how well the model fits the data. The model may fit or it may not. It seems to fit well with little deviation

Comment on whether or not the actual curve would look like the one you obtained, for a real class of real students. No there are some students that no matter how many notes thy take they would still do poorly and others that with no notes at all would still do very well.

Data Set 2

The following data represent the illumination of a comet by a certain star, reasonably similar to our Sun, at various distances from the star:

Distance from Star (AU) Illumination of Comet (W/m^2)

1 1040

2 260

3 115.5556

4 65

5 41.6

6 28.88889

7 21.22449

8 16.25

9 12.83951

10 10.4

Obtain a model.

**Y=(6.663194375)t^2-(111.0833325)t+454.9138875**

Determine from your model what illumination would be expected at 1.6 AU from the star. 294.2383331

At what range of distances from the star would the illumination be comfortable for reading, if reading comfort occurs in the range from 25 to 100 Watts per square meter?usaing the model I gave above and the quadratic formula I came up with (10.3877,25.0010) and ((4.31163,99.83346)

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. My model does not fit very well the points I picked fit but that is it . In my model (1,350) and it should have been (1,1040) and my average deviation was –198.87399

"

&#Good work. Let me know if you have questions. &#