There are 500 sheets of paper in a 2-inch ream of paper. How thick a stack would result from folding a piece of paper ten times? (It may be easier to think in terms of the paper's being cut in half and stacked rather than folded.)

Write an equation that models the height of a stack of paper with [tex]n[/tex] folds (cuts).

In this scenario, the height of a paper stack after n folds can be modeled with the equation 'Height = 0.004 * 2^n'. After 10 folds, the height of the stack would theoretically increase to approximately 4.096 inches.

Explanation:

In this problem, we are asked to model the height of a stack of paper when it is folded or cut n times. Each time the paper is cut, it effectively doubles in thickness. If we know that a 500-page (or, equivalently, 2-inch) stack of paper corresponds to a thickness of 0.004 inches per sheet, we can formulate the equation: Height = 0.004 * 2^n. This equation represents our situation, with n being the number of folds (or cuts).

For instance, if a single sheet of paper is folded or cut ten times, the number of pages in the stack would be 2^10 = 1024 sheets. This results in a stack with a height of 1024 * 0.004 inches = 4.096 inches.

Remember, this is purely theoretical and in real life, it's not possible to fold paper this many times due to physical limitations, such as the volume of the stack versus the original length and width of the paper sheet.

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