A tricycle ride cost P20.00 for the first I kilometer, and each additional per half kilometer adds P5.00 to the fare. Use a piecewise function to represent the tricycle fare in terms of the distance d in kilometers.

Let's define the tricycle fare as a piecewise function \( f(d) \), where \( d \) is the distance in kilometers.

### Given:
- The first 1 kilometer costs \( P20.00 \).
- Each additional 0.5 kilometers adds \( P5.00 \) to the fare.

### Piecewise Function:
1. For the first 1 kilometer \( (0 \leq d \leq 1) \):
   - The fare is constant at \( P20.00 \).
2. For distances greater than 1 kilometer \( (d > 1) \):
   - The fare increases by \( P5.00 \) for every additional 0.5 kilometers.

### Constructing the Function:
- When \( d \leq 1 \), the fare is \( f(d) = 20 \).
- When \( d > 1 \), the fare is calculated as:
  \[
  f(d) = 20 + 5 \times \left\lceil 2(d - 1) \right\rceil
  \]
  Here, \( \left\lceil 2(d - 1) \right\rceil \) is the ceiling function that rounds up the number of additional half-kilometers.

### Piecewise Representation:
\[
f(d) = 
\begin{cases} 
20 & \text{if } 0 \leq d \leq 1 \\
20 + 5 \times \left\lceil 2(d - 1) \right\rceil & \text{if } d > 1 
\end{cases}
\]

This piecewise function covers the fare calculation for any distance \( d \) in kilometers.

Would you like more details or have any questions?

### Related Questions:
1. How would the fare change if the initial 1 km cost was increased to P30.00?
2. What is the fare for a 3.5 km ride based on this function?
3. How does the piecewise function change if the rate per additional 0.5 km increases to P7.00?
4. Can you express this piecewise function as a continuous function?
5. What would the fare be for a fractional distance, such as 1.75 kilometers?

**Tip:** Always consider boundary conditions when constructing piecewise functions, as they determine the transitions between different segments.

Understand how to calculate tricycle fares using a piecewise function. Explore the initial cost, additional charges per half kilometer, and their mathematical representation. Suitable for Grades 10-12 students and anyone interested in piecewise functions.

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