Math 1525 Excel Lab 1 Introduction to Excel Spring, 2001

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1 Math 1525 Excel Lab 1 Introduction to Excel Spring, 2001 Goal: The goal of Lab 1 is to introduce you to Microsoft Excel, to show you how to graph data and functions, and to practice solving problems with Excel. You should not find this lab difficult, but it is lengthy, so please don t procrastinate. The examples in this lab are not optional. Example 1: (Graphing a table of data.) Consider the following table relating the quantity of items produced to the price in dollars at which each item is sold. (This represents a supply function, which we ll see later on in the course.) q p First, we need to enter the table in Excel. Fortunately, this is easy: 1. Start with a blank spreadsheet. Use the mouse to highlight the cell where you wish to start. For this example, highlight cell A1, by clicking anywhere inside that cell. 2. Key in the data including the column headings q and p into the corresponding spreadsheet cells. Use the arrow keys on the keyboard to move from one cell to the next. (This is easier than highlighting each cell with the mouse.) 3. You may change the width of each column to fit the data. To change the width of column A, point the mouse to the vertical line separating the header A from the next header B. Hold down the mouse button and drag the line while holding down the button. A shortcut is to double-click on that vertical line, which tells Excel to automatically size the column. click here

2 You ve successfully created a table in Excel. Now we ll go through the steps of graphing the table: 1. Highlight the table you ve created. To highlight a table, first position the mouse over one of the corner cells of the table. Then hold down the mouse button and drag the mouse to the diagonally-opposite corner. 2. Click on the ChartWizard icon. If you re not sure which icon is the ChartWizard, you can also click on the word Insert and drag the mouse pointer down to the word Chart. 3. A dialog box should appear which lists several different types of graphs. For every lab in 1525, we will be using the XY (Scatter) type of graph. Click on XY (Scatter). 4. To the right, we see five sample graphs. When graphing raw data, like in this example, leave the top graph highlighted (like it already is). Click on Next >. 5. Click on Next > again. The window should now read Chart Wizard Step 3 of Under the Titles tab, give your graph and axes a title. The labels for the axes should include the appropriate units when they re known. An unlabeled graph is incomplete! 7. Under the Legend tab, turn off the Show Legend option, then click Finish. You ve now created a graph to match your table! If you have completed this example successfully, you re ready to move on. price (dollars) Supply Graph quantity (units)

3 Exercise 1: Show the table and graph that would be obtained if the q and p columns in Example 1 were switched. Exercise 2: page 11, #2. For parts a and b, you need only to construct the table and create the graph. Make sure that your graph is completely labeled that is, make sure that both axes have meaningful labels and that the graph has a title that describes what it represents. Then answer part c. For part d, construct a new table and graph before answering. In other words, you should hand in two tables and two graphs for this problem. Example 2: (Graphing a formula.) Graph the function y = x 3 + 5x 2 8 over the interval [ 4, 5]. Our first step, like before, is to generate a table for this data. 1. Enter the column headings x and y. Enter the first two values for column x: 4 and Highlight the 4 and 3. Notice there is a little notch on the bottom-right corner of the area you ve highlighted. Position your mouse over that notch, and the cursor should change from a fat cross to a thin cross. Click on that notch, and hold the button down. Drag the mouse downwards until the number 5 appears and release the button. Excel will automatically fill in the rest of the column. (Note: You need two values highlighted in order to do this.) 3. Now go back to the top of the second column. We want to enter the formula x 3 + 5x 2 8 into Excel. Here s how to enter formulas: (a) Begin the formula with a = sign. That s how Excel knows you re entering a formula. (b) Instead of typing the variable x, type the cell where the value for x is located, for example, A2. (c) Enter a * every time multiplication is indicated, even if we would normally not write it. For example, 5x would be entered as 5*A2. (d) Finally, use a ^ symbol to indicate an exponent. So, 5x 2 would be entered as 5*A2^2. Using all these rules together, the formula we d type into cell B2 is: =A2^3+5*A2^2-8. Press Enter after typing the formula. Enter this formula, and Excel should calculate the value 8 as the answer.

4 4. Fortunately, we don t need to retype that formula into every cell in the column. Click back onto the formula you just entered, position your mouse over the notch in the bottom-right corner, and double-click. Excel will automatically fill in the formula to complete the table. double-click here! Now that you have a table for the function, you can graph that function. Graphing a function is almost like graphing a table there s only one small difference. 1. Highlight the table and click on the ChartWizard icon. 2. Choose the XY (Scatter Graph), but this time, choose a connected graph. We will be using unconnected graphs to represent discrete data points, and connected graphs to represent smooth formulas. 3. At step 3 of the ChartWizard, remember to label your graph and turn off the legend. Since we don t know what x and y represent, it s okay to label the axes just x and y. Click on Finish when you re done. Your finished graph should look like this. If you ve successfully completed this example, you re ready to move on. y y = x^3 + 5x^ (This example continues on the next page.) x

5 Exercise 3: Show the table along with the graphs. a. Graph the function f(x) = x 2 + 8x + 8 over the interval [ 15, 8]. b. Graph the function g(x) = 2x + 14 over the same interval. c. Find a formula for ( g)( x) d. Find a formula for ( g)( x) f by hand, and graph that function over the same interval. f o by hand, and graph that function over the same interval. Example 3: (Graphing more than one equation on the same graph.) The cost to manufacture q units of a product is given by the equation c = 2q + 20, and the revenue generated by selling those units is given by the equation r = 4q. Graph both of these equations on the same set of axes. Just like in the first two examples, we generate the table first. 1. First key in the column headings. We ll need a column for q, and we ll need columns for both c and r. So this table will have three columns. 2. Decide what values to enter in the q column. They re not given to you, so you may use your own judgement. Of course, q may not be negative. (How can you have negative items of a product?) For this example, I ll choose the interval [0,12]. 3. Enter the cost formula: =2*A2+20 at the top of that column, then double-click on its notch to fill that column. 4. Enter the revenue formula =4*A2 at the top of that column, then double-click on its notch to fill that column. Your finished table should look like the one on the right. Once you have the table, you re ready to graph it. Highlight all three columns and enter the ChartWizard. This time, leave the legend on, in order to distinguish between the two graphs. The point where the two graphs intersect, (10, 40), is called the break-even point. At that point, the revenue is enough to cover the costs of production. If we sell more than ten units, we ll enjoy a profit. If we sell less than ten units, we ll suffer a loss. see legend (dollars) Cost and Revenue quantity produced (units) c r

6 Exercise 4: The demand equation for a product is p = 900 q 2, and the supply equation for the same product is given by p = q 2. a. Graph both equations on the same axis. (Make sure the labels for the second and third column are different.) Your q values should cover the interval [0,30] and skip by 2. (In other words, enter 0 and 2 for your initial q values before dragging down.) b. Find the intersection point for the two functions. Where demand and supply intersect is called the equilibrium point. Exercise 5: Graph the following equations on the interval [ 20, 20]. You may skip by 2 when graphing these equations. a. y = x 3 b. y = x 3 8. Describe what effect the 8 has on the graph. c. y = (x + 3) 3. Describe what effect the +3 has on the graph. d. Based on your experience in parts b and c, draw a sketch of what y = (x 2) would look like.