 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum  MENU          Session 7, Part A:
Exploring Exponential Functions (40 minutes)

In This Part: Changing + to * | Introduction to Exponential Functions

 In Session 5, we learned that linear functions have constant first differences. That is, every time x increases by 1, y increases by a constant amount. In this section, we will come up with a description for another type of function: exponential functions. Note 2 Here's a table generated by a spreadsheet. The rule in the Output column is recursive: Start at 3 and add 10 each time. Here are the values in the table: If you need a refresher on how to use a spreadsheet, see the tutorial in Session 5. To generate this table in a spreadsheet using formulas, type the number "3" in cell B2, then type "=B2+10" in cell B3. Use the "Fill Down" menu command to continue the rule to cell B7. Remember that the value in a cell is what is displayed, but the formula is used to generate the value. Click on cell B4 (the cell containing "23") to see the rule that generates the table: "=B3+10". You also could have used a formula to generate the values in column A. Because the successive outputs have a constant difference of 10, these points should all lie on a line.  Problem A1 Use the spreadsheet to graph this table, then verify that all the points lie on the same line. Note 3  If you're having trouble making a graph, see the spreadsheet tutorial about graphing.   Close Tip If you're having trouble making a graph, see the spreadsheet tutorial about graphing. Problem A2 Click on cell B3 again, and change the + to * in the output rule. The rule should now read: "=B2*10", and you should see the value "30" displayed in the cell after you enter the new formula. Now use the "Fill Down" command to copy the rule into the rest of the Output column. If you have done this correctly, the final value in cell B7 should be 300,000. Describe the pattern of outputs in your spreadsheet.  Use the recursive rule to describe the table.   Close Tip Use the recursive rule to describe the table. Problem A3 Graph this table. Describe the graph      Problem A4 Predict how much higher the input would have to be for the output to be more than 1 billion. Then use the spreadsheet to find the answer.  Problem A5 Let's make another small change to the formulas on our spreadsheet and see how this change affects our graph. Click on cell B3 again, and change the * to / in the output rule. The rule should now read: "=B2/10", and you should see the value "0.3" displayed in the cell after you've entered the new formula. Now, use the "Fill Down" command to copy the rule into the rest of the Output column. Describe the pattern of outputs in your spreadsheet. Problem A6 Graph this table. Describe the graph. Problem A7 Think about the two new tables you created in Problems A2 and A5. For each table, list three numbers that will never appear in the Output column, and then explain why they will never appear there.  Can you find any types of numbers that will never appear in the Output column?   Close Tip Can you find any types of numbers that will never appear in the Output column?   Session 7: Index | Notes | Solutions | Video

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