A website subscription is popular amongst individuals in Baguio, P150 available for four months with an extra P50 fee for each day that payment is not received by the due date. Determine the piecewise function of the fee (f) dependent on the number of days not paid. 

To determine the piecewise function of the fee \( f(d) \) dependent on the number of days \( d \) the payment is late, we'll consider two scenarios:

1. When the payment is made on time (i.e., \( d = 0 \)).
2. When the payment is late (i.e., \( d > 0 \)).

### Piecewise Function:
\[
f(d) =
\begin{cases}
150 & \text{if } d = 0 \\
150 + 50d & \text{if } d > 0
\end{cases}
\]

### Explanation:

- **\( d = 0 \)**: If the payment is made on time, the fee is just the base subscription cost, \( P150 \).
- **\( d > 0 \)**: If the payment is late by \( d \) days, an additional fee of \( P50 \) per day is added to the base cost of \( P150 \). Hence, the total fee becomes \( 150 + 50d \).

### Do you want more details or have any questions?
Here are 5 related questions:

1. What is the fee if the payment is 3 days late?
2. How would the piecewise function change if the late fee were reduced to P30 per day?
3. What is the maximum fee if the payment is late by 10 days?
4. How can you graph the piecewise function to visualize the fee structure?
5. What would be the piecewise function if there was a grace period of 2 days with no late fee?

**Tip:** When working with piecewise functions, carefully define the conditions for each piece to ensure the function accurately represents the situation.

Understand how to calculate late payment fees using a piecewise function. Explore scenarios where payments are made on time or late, with a detailed breakdown of fees. Suitable for high school students learning about piecewise functions and linear functions.

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