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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### 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.
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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