To determine the tricycle fare in terms of the distance [tex]\( d \)[/tex] in kilometers, we will use a piecewise function. Here's a step-by-step breakdown:
1. For distances less than or equal to 2 kilometers:
- If the distance [tex]\( d \)[/tex] is less than or equal to 2 kilometers, the fare is a fixed amount of \[tex]$10.00.
2. For distances greater than 2 kilometers:
- When the distance \( d \) exceeds 2 kilometers, the fare consists of the base fare of \$[/tex]10.00 for the first 2 kilometers, plus an additional charge of \[tex]$8.00 per kilometer for every kilometer beyond the first 2 kilometers.
- Mathematically, if \( d > 2 \), the additional fare can be computed by \((d - 2) \times 8.00\).
- Therefore, the total fare in this case would be \(\$[/tex]10.00 + (d - 2) \times 8.00\).
Combining both cases, we get the piecewise function for the fare ([tex]\( f(d) \)[/tex]) as follows:
[tex]\[ f(d) = \begin{cases}
10.00 & \text{if } d \leq 2 \\
10.00 + (d - 2) \times 8.00 & \text{if } d > 2
\end{cases} \][/tex]
Further simplifying the second part:
[tex]\[ f(d) = \begin{cases}
10.00 & \text{if } d \leq 2 \\
10.00 + 8d - 16.00 & \text{if } d > 2
\end{cases} \][/tex]
[tex]\[ f(d) = \begin{cases}
10.00 & \text{if } d \leq 2 \\
8d - 6.00 & \text{if } d > 2
\end{cases} \][/tex]
Therefore, the piecewise function for the tricycle fare in terms of the distance [tex]\( d \)[/tex] in kilometers is:
[tex]\[ f(d) = \begin{cases}
10.00 & \text{if } d \leq 2 \\
8d - 6.00 & \text{if } d > 2
\end{cases} \][/tex]
