3. 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 (-)". a. What is the value of A when n 0? What does this mean in the situation? a = 90 the 0 will always =1 b. How many folds are needed before the area is less than 1 square inch? C. The area of another piece of paper in square inches, after n folds, is given by B = 100 · (-)". What do the numbers 100 and mean in this situation?

3. 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 (-)". a. What is the value of A when n 0? What does this mean in the situation? a = 90 the 0 will always =1 b. How many folds are needed before the area is less than 1 square inch? C. The area of another piece of paper in square inches, after n folds, is given by B = 100 · (-)". What do the numbers 100 and mean in this situation?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

### Folding Paper and Calculating Area

This problem explores how the area of a piece of paper changes when it is folded into thirds multiple times.

**Problem Statement:**

A piece of paper is folded into thirds multiple times. The area $ A $ of the paper in square inches, after $ n $ folds, is given by:

\[ A = 90 \cdot \left( \frac{1}{3} \right)^n \]

**Questions:**

a. **What is the value of $ A $ when $ n = 0 $? What does this mean in the situation?**

- When $ n = 0 $, $ A = 90 $. This indicates the original area of the paper before any folds are made.

b. **How many folds are needed before the area is less than 1 square inch?**

- This question requires determining the value of $ n $ for which $ A < 1 $.

c. **The area of another piece of paper in square inches, after $ n $ folds, is given by:**

\[ B = 100 \cdot \left( \frac{1}{2} \right)^n \]

- **What do the numbers 100 and $\frac{1}{2}$ mean in this situation?**

- $ 100 $ represents the original area of another piece of paper.
- $ \frac{1}{2} $ indicates that each fold reduces the area by half.

This problem helps in understanding exponential decay and how repeated folding affects the area of a piece of paper.

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