Question 1119393: the fee for hiring a guide to explore a cave is 700 php. A guide can only take care of a maximum of 4 persons and additional guided can be hired as needed. represent the cost of the hiring guides as a function of the number of the tourists who wish to explore the cave.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! best i can find is the floor and ceiling functions.
here's a reference.
https://www.mathsisfun.com/sets/function-floor-ceiling.html
i believe the ceiling function would apply here.
the equation would be y = 700 * ceiling(x/4).
this function applies 700 to the next heigher integer of x/4.
when x = 1, x/4 = 1/4 and the price is 1 * 700.
this continues until x = 4, where x/4 = 1 and the price is 1 * 700.
when x = 5, x/4 = 1 and 1/4 and the price is 2 * 700.
you can graph this function as shown below, using desmos.com/calculator.
in desmos.com, the ceiling function used is ceil(x/4).
the function is y = 700 * ceil(x/4).
you can see from the graph that:
when x = 0, the price is 0.
when x = 1 to 4, the price is 700.
when x = 5 to 8, the price is 1400.
when x = 9 to 12, the price is 2100.
etc.....
you have to use a function to model this.
in particular, you have to use the ceiling function.
the only alternative i know of is to use a stepwise function.
y = 0 for x = 0
y = 700 for x = 1 to 4
y = 2100 for x = 5 to 8
y = 2800 for x = 9 to 12
etc.
here's the graph using the ceiling function.
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