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The problem involves a piece of paper being cut into three equal parts and then further subdivided into three more equal parts. The goal is to determine how many squares will be present after a certain number of cuts.

From the image:
1. A giant piece of paper is divided into smaller pieces. The initial piece is cut into 3 equal parts and then each of those parts is also divided into 3 equal pieces, which suggests the paper is being split iteratively.

We need to answer a few questions based on this:
### a) Would it make sense to look for the number of pieces after 50 cuts? Why?
- Given that the paper is split into smaller parts each time, the number of pieces increases exponentially with each round of cuts. Looking for the number of pieces after 50 cuts would yield a very large number, so it might not be practical to calculate or observe this.

### b) Would this be a discrete or continuous graph?
- This situation would represent a **discrete graph** because the number of pieces of paper can only take integer values (1 piece, 3 pieces, 9 pieces, etc.). The number of pieces after each round of cuts is a finite and countable value.

### c) What would be the equation of the function?
- Since the paper is being split into 3 parts and then 3 parts again, the function that models the number of pieces (y) after a certain number of cuts (n) would likely follow an exponential form, possibly:
  
  \[
  y = 3^n
  \]
  
  Where:
  - \( y \) is the number of pieces
  - \( n \) is the number of cuts
This equation reflects how each cut multiplies the number of pieces.

Would you like a more detailed explanation of any part, or a deeper exploration of the graph or function?

Here are 5 related questions for further exploration:
1. What would the total number of pieces be after 3 cuts?
2. How does the number of pieces grow after each additional cut?
3. Could the cuts be modeled using a recursive function instead of an exponential one?
4. How would the graph of the function \( y = 3^n \) look like if plotted?
5. What assumptions are made about the cutting process?

**Tip:** Always consider whether a situation involves discrete or continuous data when determining the type of graph!

A giant piece of paper is cut into 3 equal pieces, and then each of these is cut into 3 equal pieces. How many pieces will there be after 10 cuts, 20 cuts, or even 50 cuts?

Explore how cutting a piece of paper into three equal parts and repeating the process leads to exponential growth. Learn to calculate the number of pieces after 10, 20, or 50 cuts using the formula y = 3^n, where n represents the number of cuts. Suitable for Grades 9-12.

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