A large on folded flag has an area of 2048 cm^2 and is folded into fourths, and then fourths again, and so on. Record the area of a region of the flag after each fold.

Describe the pattern of change in the table and write an equation between the area of a region a and the number of folds n.

a = 2048 × (¼)^n

Step-by-step explanation:

Area after a fold is ¼th of the previous area

One fold: a = 2048 × ¼

Two folds: a = (2048 × ¼) × ¼

= 2048 × (¼)²

Three folds: a = (2048 × (¼)²) × ¼

= 2048 × (¼)³

a = 2048 × (¼)^n

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