A mall charges 25pesos for the first hour or a fraction of an hour as parking fee. An additional 25pesos is charged for every additional hour, or a fraction of an hour of parking. The parking area operates from 7A.M. to 12 midnight every day.
a. Write a function rule for the problem
b. Describe the domain and the range.
c. How much will be charged to a car owner who parked a car from 7A.M. to 1:30P.M?
d. How much will be charged to a car owner who parked a car from 8:30A.M. to 11:15P.M?
Pls answer...plsss
How to describe the domain and the range?
A mall charges ₱25 for the first hour or a fraction of an hour as parking fee. An additional ₱25 is charged for every additional hour, or a fraction of an hour of parking. The parking area operates from 7:00 A.M. to 12 midnight every day.
a. To write a function rule for this problem, we first need to define the variables involved. Let's say "x" represents the total number of hours or fractions of an hour a car is parked. The function rule can then be defined as:
f(x) = 25 + 25(x - 1)
In this equation, 25 represents the initial charge for the first hour or fraction of an hour, and 25(x - 1) calculates the additional charge for each additional hour or fraction of an hour.
b. The domain of this function is the set of all non-negative real numbers greater than or equal to zero since the number of hours parked cannot be negative. Therefore, the domain is [0, ∞).
The range of this function represents the set of all possible values for the charges. Since the parking fee increases by 25 pesos for each additional hour or fraction of an hour, the range is given by the set of all positive multiples of 25, starting from 25 pesos. Therefore, the range is [25, ∞).
c. To calculate how much will be charged to a car owner who parked a car from 7 A.M. to 1:30 P.M., we need to determine the total number of hours or fractions of an hour the car was parked. The time period from 7 A.M. to 1:30 P.M. is a total of 6 hours and 30 minutes, which can be written as 6.5 hours.
Using the function rule, we can calculate the charge:
f(6.5) = 25 + 25(6.5 - 1)
= 25 + 25(5.5)
= 25 + 137.5
= 162.5 pesos
Therefore, the car owner will be charged 162.5 pesos.
d. To calculate the charge for a car owner who parked a car from 8:30 A.M. to 11:15 P.M., we need to determine the total number of hours or fractions of an hour the car was parked. The time period from 8:30 A.M. to 11:15 P.M. is a total of 14 hours and 45 minutes, which can be written as 14.75 hours.
Using the function rule, we can calculate the charge:
f(14.75) = 25 + 25(14.75 - 1)
= 25 + 25(13.75)
= 25 + 343.75
= 368.75 pesos
Therefore, the car owner will be charged 368.75 pesos.
y = 25+25*[[x]]
where [[x]] is the greatest integer less than x.