A piece of paper is folded into thirds multiple times. The area, A, of the piece of paper in square inches, after n folds, is .A = 90 (1/3)^n 1,

A piece of paper is folded into thirds multiple times. The area, A, of the piece of paper in square inches, after n folds, is .A = 90 `(1/3)^"n"`

1. What is the value of A when n = 0 ? What does this mean in the situation?
2. How many folds are needed before the area is less than 1 square inch?
3. The area of another piece of paper in square inches, after n folds, is given by B = 100 `(1/2)^"n"` What do the numbers 100 and 1/2 mean in this situation?

Solution 1: The value of A is 90 square inches. It means that when the piece of paper is folded 0 times, the area will be 90 square inches.


Solution 2: The area will be less than 1 square inch, when the number of folds will be 5.

Plug in n = 5, in the equation A = 90.`(\frac{1}{3})^{5}`

To get

A = 90.`(\frac{1}{3})^{5}` `\approx` 0.37 square inches

A = 90.`(\frac{1}{3})^{4}` `\approx` 0.37 square inches

Solution 3: The number 100 means that the piece of the paper was initially 100 square inches, and the number `\frac{1}{2}` means that the area decreases by a factor of `\frac{1}{2}` for every fold. `\frac{1}{2}` represents the common decay factor.