In this section, a table is used to create exponential growth graphs. A calculator is helpful.

Refer to the previous section’s paper folding activity or repeat it.

  1. Fold a sheet of paper in half as many times as possible.
  2. After each fold, record the information in the chart. Move your mouse over the blanks to reveal the answers.
Number of Folds (n) Area of Each Region Relative to the whole sheet of paper
1 1/2
2 1/4
3 ____
4 ____
5 ____
6 ____

The area of each region is ____ as the number of folds increases.

Review the following graphs. Select the one representing the relationship between the number of folds and Area of Each Region Relative to the whole sheet of paper. {Hint: Convert the 2nd column to decimals to match graphs.} After selecting the graph, read the descriptions of each graph below.

A: Graph of Linear with positive slope; B: Graph of a quadratic opening up; C: Graph of exponential growth; D:Graph of exponential decay

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Click here for feedback for Answer A

Linear function not matching the table
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Click here for feedback for Answer B

Quadratic not matching the table
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Click here for feedback for Answer C

Exponential growth graph the opposite of the table
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Click here for feedback for Answer D

Exponential decay represented by table and y equals one-half to the x power
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In this situation, where do you think the 1/2 comes from in the equation y = (1/2)x? ____ .

The area of each region is ____ as the number of folds increases.

This activity might not be viewable on your mobile device.Interactive exercise. Assistance may be required. Click here to see more exponential functions. Use the sliders to change the exponential functions and then look at the graphs created.