Graphing Difference Equation in Excel - Lecture Notes | MATH 130, Assignments of Mathematics

Material Type: Assignment; Professor: Clark; Class: Math Modeling Precalculus I; Subject: Mathematics; University: Hollins University; Term: Spring 1997;

Typology: Assignments

Pre 2010

Uploaded on 08/18/2009

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Math 130 Spring 2009
Graphing Difference Equations in Excel
Example: Average Daily Petroleum Consumption ’97-‘07
1. Open the Excel Worksheet Diffeq.xls. Notice that the table with our data is already in
cells A2-B13.
2. To make a graph from this table, first select(highlight) the entire table:
3. Select Insert from the Ribbon, then Scatter, then the first option of the third row as
shown here:
4. The plot should appear. You can drag a corner to enlarge or shrink. You can also
move the entire graph if you need to.
5. Now use Excel to find the difference in average daily oil consumption each year. In
other words – find C1998 – C1997, and C1999 – C1998, etc. Store these values in K4-K12 (the
column is already labeled Differences).
Click in cell K4.
Type: an “=” to tell Excel that you are starting a formula.
Then click in cell B4 (which contains C1998 = 74,053).
Type a minus sign (-),
Then click in cell A4 (which contains C1997 = 73,427).
Hit Enter.
Make sure the correct difference appears in cell K4. If it does, then ‘drag down’ through
cell K12. You should see the differences for all years 1998-2007.
6. Since the last difference is negative – we don’t want to include the year 2007 in our
model. So let’s delete it from our graph. Click anywhere in the graph, then highlight
cells A13-B13 (containing the data ’07 and 85,802), then hit your Delete key. This
should remove this point from your graph. Did it?
Excel graphing I Page 1
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Graphing Difference Equations in Excel

Example: Average Daily Petroleum Consumption ’97-‘

  1. Open the Excel Worksheet Diffeq.xls. Notice that the table with our data is already in cells A2-B13.
  2. To make a graph from this table, first select(highlight) the entire table:
  3. Select Insert from the Ribbon, then Scatter , then the first option of the third row as shown here:
  4. The plot should appear. You can drag a corner to enlarge or shrink. You can also move the entire graph if you need to.
  5. Now use Excel to find the difference in average daily oil consumption each year. In other words – find C 1998 – C 1997 , and C 1999 – C 1998 , etc. Store these values in K4-K12 (the column is already labeled Differences ). Click in cell K. Type: an “ = ” to tell Excel that you are starting a formula. Then click in cell B4 (which contains C 1998 = 74,053). Type a minus sign ( - ), Then click in cell A4 (which contains C 1997 = 73,427). Hit Enter****. Make sure the correct difference appears in cell K4. If it does, then ‘drag down’ through cell K12. You should see the differences for all years 1998-2007.
  6. Since the last difference is negative – we don’t want to include the year 2007 in our model. So let’s delete it from our graph. Click anywhere in the graph, then highlight cells A13-B13 (containing the data ’07 and 85,802), then hit your Delete key. This should remove this point from your graph. Did it?
  1. Now let’s create a graph of our first model for this data. In class we decided to start the difference equation: C n+1 = C n +626, C 0 = 73,427 as our first model. Why did we use the number 626? Why did we use the number 73,427?
  2. Use Excel to enter the model/(prediction) values in column C: a) Type the starting value 73427 (no comma) in cell C3. b) Type ‘ = 626 + ’ then click in cell C3 , then hit Enter****. c) Drag down through cell C12.
  3. To get a better idea of whether or not this model is “good” – we need to see the graph. So – let’s add the model to our graph. a) Click anywhere in your graph. b) Blue square handles should appear around your data (cells B3-B12): c) Grab the lower right blue handle and drag until you have included the data from Model 1 in the blue rectangle: An additional curve (labeled Model 1) should appear in your graph.
  4. Based on the graph – is this a good model? How could we improve it?
  5. Try a second model. This time, use the difference equation: C n+1 = C n +1674, C 0 = 73,427. Use Excel to find the predicted values for this model and store them in column D. Then add this curve to the graph. You will need to adjust the scale on your vertical axis after you add the curve this time. To do this:

d) Use Excel to add the curve for this model to your graph. Is this model an improvement over the previous one? Explain.

  1. Let’s try one more model – change the starting value to 72,000 but use the average difference (1392) as the constant difference in your model. This time your difference equation should be C n+1 = C n + 1382 , C 0 = 72,000. Store your model in Column G. Add the curve for this model to your graph. Is this model better than any of the previous ones? Explain.
  2. Save your work: Select FileSave As then decide whether you will always be working with Excel 2007 or sometimes will use Excel
    1. Click the drop-down arrow in the Save-in box, select your H drive and then type an appropriate new name in the Filename box. It would be helpful for you to include your name in the filename. ( Diffeq JaneSmith for example). Then click Save.
  3. Email the file to [email protected] as an attachment so that I can take a look and make sure that you’re having no problems. Note that “Page 2” of this spreadsheet has some helpful tables set-up for you for your graphing homework.