Answer :
Certainly! Let's go through a step-by-step process of determining the thickness of a piece of paper after several folds.
### Initial Thickness
The starting thickness of the paper is given as 0.01 centimeters (cm).
### Understanding the Folding Process
Each time you fold the paper, its thickness doubles. For example:
- 1 fold will double the thickness to [tex]\(0.02\)[/tex] cm.
- 2 folds will double it again, and so on.
### Calculating the Thickness
1. After 4 Folds:
- Start with the initial thickness of the paper: [tex]\(0.01\)[/tex] cm.
- Since each fold doubles the thickness, after 4 folds, the thickness is calculated as:
[tex]\[
\text{Thickness after 4 folds} = 0.01 \times (2^4)
\][/tex]
- Calculate [tex]\(2^4 = 16\)[/tex].
- So, the thickness is [tex]\(0.01 \times 16 = 0.16\)[/tex] cm.
2. After 5 Folds:
- Again, start with the initial thickness: [tex]\(0.01\)[/tex] cm.
- After 5 folds, the thickness is:
[tex]\[
\text{Thickness after 5 folds} = 0.01 \times (2^5)
\][/tex]
- Calculate [tex]\(2^5 = 32\)[/tex].
- So, the thickness is [tex]\(0.01 \times 32 = 0.32\)[/tex] cm.
### Summary
- The thickness of the paper after 4 folds is [tex]\(0.16\)[/tex] cm.
- The thickness of the paper after 5 folds is [tex]\(0.32\)[/tex] cm.
These results show how the thickness increases exponentially with each fold due to the doubling process.
### Initial Thickness
The starting thickness of the paper is given as 0.01 centimeters (cm).
### Understanding the Folding Process
Each time you fold the paper, its thickness doubles. For example:
- 1 fold will double the thickness to [tex]\(0.02\)[/tex] cm.
- 2 folds will double it again, and so on.
### Calculating the Thickness
1. After 4 Folds:
- Start with the initial thickness of the paper: [tex]\(0.01\)[/tex] cm.
- Since each fold doubles the thickness, after 4 folds, the thickness is calculated as:
[tex]\[
\text{Thickness after 4 folds} = 0.01 \times (2^4)
\][/tex]
- Calculate [tex]\(2^4 = 16\)[/tex].
- So, the thickness is [tex]\(0.01 \times 16 = 0.16\)[/tex] cm.
2. After 5 Folds:
- Again, start with the initial thickness: [tex]\(0.01\)[/tex] cm.
- After 5 folds, the thickness is:
[tex]\[
\text{Thickness after 5 folds} = 0.01 \times (2^5)
\][/tex]
- Calculate [tex]\(2^5 = 32\)[/tex].
- So, the thickness is [tex]\(0.01 \times 32 = 0.32\)[/tex] cm.
### Summary
- The thickness of the paper after 4 folds is [tex]\(0.16\)[/tex] cm.
- The thickness of the paper after 5 folds is [tex]\(0.32\)[/tex] cm.
These results show how the thickness increases exponentially with each fold due to the doubling process.
