A bakery has a pricing of 10 pcs of pandesal for 50 PHP; however there is an increase of 2 PHP, for each additional piece of bread. Determine the piecewise function of number of the cost(c) dependent on the number of pandesals.

To determine the piecewise function for the cost \( c(n) \) of buying \( n \) pieces of pandesal, given the pricing structure, we can break the problem down into different scenarios based on the number of pandesals purchased.

### Given:
- The first 10 pieces cost a total of 50 PHP.
- For each additional piece beyond 10, the price increases by 2 PHP per piece.

### Let's define the piecewise function:

\[
c(n) =
\begin{cases} 
50 & \text{if } 0 \leq n \leq 10 \\
50 + 2(n - 10) & \text{if } n > 10 
\end{cases}
\]

### Explanation:
- **For \( 0 \leq n \leq 10 \)**: The cost is fixed at 50 PHP, regardless of the number of pieces.
- **For \( n > 10 \)**: The cost is 50 PHP for the first 10 pieces, plus an additional 2 PHP for each piece beyond 10.

So, the piecewise function accurately models the cost \( c(n) \) based on the number of pandesals purchased.

Would you like more details on how to graph this function or any further clarifications?

### Additional Questions:
1. How would you graph this piecewise function?
2. What would be the cost for 15 pieces of pandesal?
3. How does the function change if the initial price for 10 pieces increases?
4. What if the cost for each additional piece was 3 PHP instead of 2 PHP?
5. How does this piecewise function relate to linear functions?

### Tip:
When working with piecewise functions, always carefully define the conditions for each piece to ensure the function accurately reflects the scenario.

Learn how to calculate the cost of pandesal at a bakery using a piecewise function. Understand the pricing structure of 10 pieces for 50 PHP with a 2 PHP increase per additional piece. Suitable for high school students.

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