Question

7. A van rental charges P5,500.00 flat rate for a whole-day tour in CALABARZON of
5 passengers and each additional passenger added P500.00 to the tour fare.
Express a piecewise function to show to represent the van rental in terms number
of passenger n.
Answer:​

Answer 1

Given :- A van rental charges P5,500.00 flat rate for a whole-day tour in CALABARZON of 5 passengers and each additional passenger added P500.00 to the tour fare. Express a piecewise function to show to represent the van rental in terms number of passenger n.

Answer :-

given that, van rental charges for 5 passengers is P5500.

So,

→ Number of passengers = less than or equal to 5.

→ Total charge = P5500 .

Than,

→ 5500 for n ≤ 5.

Now, given that, each additional passenger added P500 to the tour fare.

and, Total passengers are n.

Than,

→Total charge = charges for 5 passenger + charges for more than 5 members with each paying P500

→ Total passengers = n .

Therefore,

→ Total charge = 5500 + 500(n - 5) where n > 5.

Hence,

→ Required piecewise function of total charge = 5500 + 500(n - 5) where n > 5.

=> 5500 + 500n - 2500 where n > 5 .

=> 3000 + 500n where n > 5. (Ans.)

So, piecewise function are :-

→ 5500 n ≤ 5.

→ 3000 + 500n n > 5.