A van rental charges 5,500.00 pesos flat rate for a whole-day tour in CALABARZON of 5 passengers and each additional passenger added 500.00 pesos to the tour fare. Express a piecewise function to show to represent the van rental in terms number of passengers n.
5500 for n <= 5
5500 + 500n for n > 5
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5,500 if n <= 5
5,500 it 500(n-5) if n > 5
Solution?
To express the van rental as a piecewise function in terms of the number of passengers, we need to consider two cases:
Case 1: When there are 1 to 5 passengers.
In this case, the flat rate of 5,500.00 pesos applies, regardless of the number of passengers.
Cost for 1 to 5 passengers: 5,500.00 pesos
So, the function for this case is:
f(n) = 5,500.00
Case 2: When there are more than 5 passengers.
In this case, there is an additional charge of 500.00 pesos for each passenger beyond the initial 5.
For each additional passenger beyond 5, the cost increases by 500.00 pesos.
So, the function for this case is:
f(n) = 5,500.00 + (n - 5) * 500.00
To summarize, the piecewise function for the van rental in terms of the number of passengers (n) is:
f(n) = 5,500.00 for 1 ≤ n ≤ 5
f(n) = 5,500.00 + (n - 5) * 500.00 for n > 5