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Patterns, Functions, and Algebra
 
Session 7 Part A Part B Part C Part D Homework
 
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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:

table of values

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.

table of formulas

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

Solution  

Use the spreadsheet to graph this table, then verify that all the points lie on the same line. Note 3


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
If you're having trouble making a graph, see the spreadsheet tutorial about graphing.   Close Tip

 

Problem A2

Solution  

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.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Use the recursive rule to describe the table.   Close Tip

 

Problem A3

Solution  

Graph this table. Describe the graph


Take it Further

Problem A4

Solution  

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

Solution  

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

Solution  

Graph this table. Describe the graph.


 

Problem A7

write Reflect  

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.


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Can you find any types of numbers that will never appear in the Output column?   Close Tip

Next > Part A (Continued): Introduction to Exponential Functions

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