1 You are planning a reunion event with some high school fri

1) You are planning a reunion event with some high school friends. You are going to rent an event hall and everyone will split the cost evenly. For example, if the hall costs $1200 and there are 50 people attending, each will pay $24. The total cost of the event is determined as follows: the hall charges for the hall rental then adds a per person charge for each person in attendance. Assume the rental cost is $750 and the per person charge is $35 for each person in attendance. Write a rational function, f(x), which determines the evenly split cost per person where x is the number of people in attendance. Please note: the cost per person IS NOT the $35 that the hall charges per person. Then answer these questions about the situation described: a) find the horizontal asymptote or end behavior of the function f(x); b) in practical terms, what does the end behavior/horizontal asymptote describe in terms of the situation; and, c) the rational function you determine is a continuous function (except where there is a vertical asymptote). In practical terms, would the situation described actually be a continuous function? Why or why not?

Solution

Fixed Cost = 750 $ ( Cost of Hall)

Variable Cost = 35$ (depending upon number of people attending the function)

Hence the Total cost of the program will be equal to

=> Fixed Cost + Variable Cost

=> 750 + 35x (where x is the number of people attending the function)

Cost Per Person attending the function will be equal to

=> Total cost/x = (750 + 35x)/x = 750/x + 35

a) To find the horizontal asymptote, put x = very big number

hence the end behavior of the function f(x) = 35 (when x is very large)

b) In practical terms, the number of people attending the party are very large, hence the cost of hall rent is negligible in terms of overhead cost

c) Vertical asymptote occurs when x is zero, that condition will never happen since if there is no one attending the party then there will be no need to arrange the function as well