Question

a van rental charges 5500 flat rate for a whole-day tour in calabarzon of 5 passenger and each additional passenger added 500 to the tour fare. express a piecewise function to show to represent the van in terms number of passenger n.​

Answer 1

Given:

A van rental charges 5500 flat rate for a whole-day tour in calabarzon of 5 passenger.

Each additional passenger added 500 to the tour fare.

To find:

The piecewise function to show to represent the van in terms number of passenger n.​

Solution:

Let f(n) be the tour fare of n number of passengers.

Number of passengers cannot be negative or faction values. So, n is always greater than or equal to 0 and whole number.

A van rental charges 5500 flat rate for a whole-day tour in calabarzon of 5 passenger.

For
`0\leq n\leq 5`,

`f(n)=5500`

Each additional passenger added 500 to the tour fare.

For
`n>5`

`f(n)=5500+500(n-5)`

Therefore, the required piecewise function is
`f(n)=\begin{cases}5500, & \text{ if } 0\leq n\leq 5\\ 5500+500(n-5), & \text{ if } n>5\end{cases}`.