Question

Suppose you were able to take a large piece of paper of ordinary thickness and fold it in half 50 times. what would the height of the folded paper be? would it be less than a foot? about one yard? as long as a street block? as tall as the empire state building? taller than mount everest?

Answer 1

To find the height of the folded paper, we can use the formula: Final height = (Original height) / 2⁵⁰. Assuming the original height is 1 foot (12 inches), the final height is approximately 5.42 x 10⁻¹⁶ inches. Therefore, the height of the folded paper would be much smaller than a foot or any other comparison provided.

Step-by-step explanation:

To find the height of the folded paper, we can start by considering the dimensions of a folded piece of paper. When you fold a piece of paper in half, you reduce its height by half, but its width remains the same. So, after one fold, the height is half of the original height. After two folds, the height is half of the height after the first fold, and so on.

Since the paper is folded 50 times, we can use the formula:

Final height = (Original height) / 2⁵⁰

Assuming the original height of the paper is 1 foot (12 inches), we can calculate the final height as:

Final height = 12 / 2⁵⁰

Calculating this value gives an extremely small number, approximately 5.42 x 10⁻¹⁶ inches. So, the height of the folded paper would be much smaller than a foot, yard, street block, the Empire State Building, and Mount Everest.

Answer 2

see the attached table

the function will be

y=2^n
n= number of folds
y= thick (number of sheets)

the answer is

the height of the folded paper will be 4.50 E+12 in------> 1.62 E+13 m

the result obtained exceeds all the comparisons indicated in the problem (see the attached table)