Question

A school principal is planning a field trip to a museum. A charter bus company charges $120 plus $5 per passenger for transportation to and from the museum. Admission to the museum costs $8 per person. The principal uses function f to model the cost, in dollars, of transporting x people to and from the museum and function g to model the cost, in dollars, of admission to the museum for x people. What are the two functions?

f(x) =

Answer 1

The function f(x) for the transportation cost is represented as f(x) = $120 + $5x, and the function g(x) for the museum admission cost is g(x) = $8x. These functions help to determine the entire cost of the field trip for any number of attendees.

Step-by-step explanation:

When solving the mathematical problem presented in the school principal's scenario, we define two functions. The first function, f(x), models the transportation cost to and from the museum for x people. The bus company is charging a flat fee of $120, plus $5 per passenger. Therefore, our function f(x) will be:

f(x) = $120 + $5x

The second function, g(x), represents the cost of admission to the museum for x people. As the admission fee is $8 per person, the function g(x) should reflect the total cost for x persons. The formulation of the function g(x) will be:

g(x) = $8x

With functions f(x) and g(x), the principal can now predict the total cost of the field trip, by summing the costs of both transportation and admission for any given number of students and chaperones attending.