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(h) dependent on the number of pandesals(p).

To express the cost \( h(p) \) as a piecewise function dependent on the number of pandesals \( p \), we'll consider two different scenarios based on the number of pandesals purchased.

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

### Piecewise Function:
\[
h(p) =
\begin{cases} 
50 & \text{if } 0 \leq p \leq 10 \\
50 + 2(p - 10) & \text{if } p > 10 
\end{cases}
\]

### Explanation:
- **For \( 0 \leq p \leq 10 \)**: The cost \( h(p) \) is a flat rate of 50 PHP, no matter how many pieces are bought within this range.
- **For \( p > 10 \)**: The cost \( h(p) \) is 50 PHP plus an additional 2 PHP for each pandesal beyond the first 10. The term \( 2(p - 10) \) accounts for the extra cost of additional pieces.

### Examples:
- **If \( p = 8 \)**: \( h(p) = 50 \) PHP (since \( p \leq 10 \)).
- **If \( p = 12 \)**: \( h(p) = 50 + 2(12 - 10) = 50 + 4 = 54 \) PHP.

This piecewise function models the cost of pandesals based on how many you buy.

Would you like more examples, a graph of this function, or any other details?

### Additional Questions:
1. What is the cost for 20 pandesals using this function?
2. How would the function change if the initial 10 pieces were priced at 60 PHP instead?
3. How would you graph this piecewise function?
4. What is the interpretation of the slope in the second part of the function?
5. What if the price increase was 3 PHP per additional piece instead of 2 PHP?

### Tip:
When constructing piecewise functions, ensure that the boundaries between different cases are clear and the conditions cover all possible inputs.

Understand how to calculate the cost of pandesals using a piecewise function based on the number of pieces purchased. This problem involves understanding piecewise functions and linear functions. Suitable for Grades 7-9.

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