Question
What is the total cost of a 10 km jeepney ride using a piecewise function?
Answers
GPT-4o mini
To model the total cost of a 10 km jeepney ride using a piecewise function, we first need to understand the typical fare structure for jeepneys in the Philippines (as an example). Jeepney fares usually have a base fare for the first few kilometers, plus an additional fare for each kilometer after that.
Let's assume the following fare structure:
- Base fare: 12 PHP for the first 4 km
- Additional fare: 1.50 PHP for each kilometer beyond the first 4 km
Now, we can define the piecewise function for the total cost \( C(d) \), where \( d \) is the distance in kilometers:
\[
C(d) =
\begin{cases}
12 & \text{if } d \leq 4 \\
12 + 1.50 \times (d - 4) & \text{if } d > 4
\end{cases}
\]
Now, to calculate the cost for a 10 km ride, we use the second part of the piecewise function since 10 km is greater than 4 km:
1. Calculate the distance beyond the first 4 km:
\( d - 4 = 10 - 4 = 6 \) km
2. Calculate the additional cost for those extra 6 km:
\( 1.50 \times 6 = 9 \) PHP
3. Add this to the base fare:
\( C(10) = 12 + 9 = 21 \) PHP
Therefore, the total cost of a 10 km jeepney ride is **21 PHP**.
Let's assume the following fare structure:
- Base fare: 12 PHP for the first 4 km
- Additional fare: 1.50 PHP for each kilometer beyond the first 4 km
Now, we can define the piecewise function for the total cost \( C(d) \), where \( d \) is the distance in kilometers:
\[
C(d) =
\begin{cases}
12 & \text{if } d \leq 4 \\
12 + 1.50 \times (d - 4) & \text{if } d > 4
\end{cases}
\]
Now, to calculate the cost for a 10 km ride, we use the second part of the piecewise function since 10 km is greater than 4 km:
1. Calculate the distance beyond the first 4 km:
\( d - 4 = 10 - 4 = 6 \) km
2. Calculate the additional cost for those extra 6 km:
\( 1.50 \times 6 = 9 \) PHP
3. Add this to the base fare:
\( C(10) = 12 + 9 = 21 \) PHP
Therefore, the total cost of a 10 km jeepney ride is **21 PHP**.