Question

A piece of paper is 8.5in by 11n. Imagine repeatedly folding the paper in half. What happens to the area of paper after each fold? Write an exponential function to find the area of paper after each fold.

Answer 1

A(n) = 93.5 / 2^(2n-1)

Explanation:

Each time the paper is folded in half, its length and width are halved. Therefore, the area of the paper is also halved after each fold.

Let A₀ be the initial area of the paper, which is 8.5 inches by 11 inches, or 93.5 square inches (rounded to one decimal place). After the first fold, the area becomes:

A₁ = (8.5/2) x 11 = 46.75 square inches

After the second fold, the area becomes:

A₂ = (8.5/2) x (11/2) = 23.375 square inches

And so on.

Therefore, the exponential function to find the area of the paper after each fold is:

A(n) = 93.5 / 2^(2n-1)

Answer 2

A = (93.5/2^(2n)) After each fold, the area of the paper is halved.

Explanation:

When the paper is folded in half, the length and width of the paper are each halved, which means that the area of the paper is also halved. If we continue to fold the paper in half, the area will continue to be halved with each fold.

To write an exponential function to find the area of the paper after each fold, we can use the formula for the area of a rectangle, A = lw, where A is the area, l is the length, and w is the width. Since the length and width are both halved with each fold, we can represent this as:

A = (8.5/2^n)(11/2^n)

where n is the number of folds. To simplify this, we can combine the terms under the same exponent and get: