Spreadsheets are useful for calculating and graphing problems using big numbers, such as the following:

Problem: Alex is painting pictures for an art show. The first picture took 1 minute to paint. The second picture took 2 minutes, the third took 4 minutes, the fourth took 8 minutes, the fifth took 16 minutes and so on. Alex wants to have 25 pictures in his art show. How long will it take him altogether to get ready for his show? Use the largest possible (sensible) unit when you give your final answer..

Instead of using a calculator to figure out the doubling pattern in the minutes, use a spreadsheet. Open up a word-processing document. Turn on the tool panel and insert a two column, thirty row spreadsheet. Put the labels in as shown in the example. Enter your first pair of data values in cells A2 and B2. The picture number will be one (1) and the time it takes to paint it in minutes will be one (1).

Next, write a formula for cell A3. The next picture number is 2, then 3, then 4, and so on. So, your formula for cell A3 should be equal to the data in A2 plus one (1). Write the formula and enter it cell A3. Don't forget to start with an equal sign since it's a formula.

Now, highlight cells A3 through A26. Then choose the Calculate pulldown menu and select Fill Down. The entire set of picture numbers should appear.

Write the formula for B3 and fill it down through cell B26. Remember, it's a different formula. This time, you take the value in B2 and double it. After filling down, the entire set of minute values should appear.

At this point, your spreadsheet should look like this.

A formula must now be written in cell B27 to calculate the total time it took Alex to paint all those pictures. What do you do? Hint: add!

Your next goal is to express the answer using the largest sensible units. You would never speak about thirty-three million, five hundred and fifty-four thousand, four-hundred and thirty-one minutes in normal conversation! So, we shall first change minutes to hours and see if it makes sense. Then, we can go to days and then years if necessary. Write a formula in B28 to turn the minute data in B26 into hours. In B29, change the hours to days. In B30, convert the days to years. Hint: divide!

How long (in years) does it take Alex to paint the 25 pictures? Give your answer in a solution statement. Write it beside your chart.

Finally, let's graph this relationship. Highlight cells A1 through B26. Make sure you get them all. Then go up to the Options pulldown menu and choose Make Chart. Use and x,y line graph. Move your graph to the bottom of your page. Notice how the computer knew to put your left column, the x values, on the x axis. It knew to put the right column on the y axis. It has also labeled your axes since you highlighted the labels at the top of the chart.

Your graph should look like this:

To finish off this activity, explain what this graph is showing you. Write your text below the graph. What does it mean when you see a curve shooting up after it's been pretty flat for awhile? What does this mean about how the y value (minutes) is behaving in relationship to the x value (picture number)?