qa3

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course Mth 173

1/24 9:22 p.m.

003.

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Question: `qNote that there are four questions in this assignment.

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Question: `q001. Sketch a graph similar to that you constructed for the stock values, this time for the depth of the water vs.

clock time (depths 80, 40, 20 at clock times 10, 40, 90). Your first point, for example, will be (10, 80). Connect these

points with straight lines and determine the slopes of the lines.

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Your solution:

1st slope, -40/30, -4/3

2nd slope, -20/50, -2/5

confidence rating #$&*: 3

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Given Solution:

`aThe three points are (10, 80), (40, 40) and (90, 20).

From the first point to the second the rise is from 80 to 40, or -40, and the run is from 10 to 40, or 30. So the slope is -40 /

30 = -1.33.

From the second point to the third the rise is from 40 to 20, or -20, and the run is from 40 to 90, or 50, so the slope is -20 /

50 = -.4. Click on 'Next Picture' to see graph.

`routine graph3

???what 'next picture' I see no links

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Self-critique (if necessary):OK

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Self-critique Rating:OK

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Question: `q002. Look at your results for the slopes, and look the results for the average rates of change. What do you

notice? In what way then does the graph represent the average rate of change?

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Your solution:

as time increases depth of water decreases, The more time has past, the more gentle the slope becomes

Im not sure how to properly explain it, but I imagine true data as a scatter plot, and when we draw a straight line, its like

finding the average, and if you move around a graph, your making a change, therefore it is the average change when you do a

straight line between two points.

confidence rating #$&*:2

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Given Solution:

`aThe slopes and the rates of change are numerically equal. For example between the second and third points the rise of -20

represents the -20 cm change in depth and the run of 50 represents the 50 seconds required to make this change, so the

slope represents the -20 cm / (50 sec) average rate of change over the second time interval. We therefore see that slope

represents average rate of change.

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Self-critique (if necessary):

???I didnt view them as two separate things, should I see them as separate, or they always the same?

@&

The slope is a characteristic of a graph, and the rate of change is a characteristic of some system or model.

The slope represents the rate of change, but is not strictly the same thing as the rate of change.

*@

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Self-critique Rating:2

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Question: `q003. To what extent do you think your graph with three points and straight line segments between them

accurately depicts the detailed behavior of the water over the 80-second period of observation?

How do you think the actual behavior of the system differs from that of the graph?

How do you think the graph of the actual behavior of the system would differ from that of the graph you made?

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Your solution:

From the graph itself, I can only make assumptions, and generalizations, nothing specific for that certain graph. The only

detail is the more time is allowed to pass, the rate that depth decreases seems to decrease

???am I allowed to assume this, the graph just says time and depth, what if someone adds water to this, what if this is a in the

ground, with a pipe feeding water out, and they dig more of the ground up, or fill in the bottom some.

@&

The model applies to water flowing from a hole below the water surface. The depth of the water changes in a smooth and predictable manner, so for this situation the graph does an excellent job of predicting the behavior of the system.

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confidence rating #$&*:

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Given Solution:

`aThe straight line segments would indicate a constant rate of change of depth. It is fairly clear that as depth decreases, the

rate of change of depth will decrease, so that the rate of change of depth will not be constant. The graph will therefore never

be straight, but will be a curve which is decreasing at a decreasing rate.

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Self-critique (if necessary):OK

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Self-critique Rating:OK

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Question: `q004. From the given information, do you think you can accurately infer the detailed behavior of the water depth

over the 80-second period? Do you think you can infer the detailed behavior better than you could the values of the stocks?

Why or why not?

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Your solution:

as long as it keeps decreasing, and no one is adding, etc it should decrease at a decreasing rate. I should be able to detail

almost exactly what happened., Knowing how this would react in the real world. I believe this is a ""law"" that will always

happen, therefore detailed behavior could be better determined than stocks, that are man made and can do what they want,

they have no true ""law"" they must always follow.

confidence rating #$&*:2

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Given Solution:

`aIt will turn out that three data points will be sufficient to infer the detailed behavior, provided the data are accurate.

However you might or might not be aware of that at this point, so you could draw either conclusion. However it should be

clear that the behavior of the water depth is much more predictable than the behavior of the stock market. We don't know

on a given day whether the market will go up or down, but we do know that if we shoot a hole in the bottom of a full bucket

the water level will decrease, and we expect that identical holes in identical buckets should result in the same depth vs. clock

time behavior.

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Self-critique (if necessary):OK

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Self-critique Rating:OK

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&#This looks good. See my notes. Let me know if you have any questions. &#