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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e35cc01-e960-42d9-b2dd-1006cdd5ad4c%2F2e9fc692-1a29-4527-856e-46f0a0dd22b4%2Fcwz0b67_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### 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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