Question

The cost per guest of catering an event of no more than 100 people is modeled by the function f(x) = 20 + 5x. The number of guests is modeled by the function g(x) = 100 −x , where x represents the number of guests fewer than 100 that attend. Evaluate(f ∙g )(18) and interpret what it means in the context of the problem.

Answer 1

To evaluate (f ∙ g)(18), substitute 18 into both functions f(x) and g(x) and then multiply the results. In the context of the problem, (f ∙ g)(18) represents the cost per guest for an event where 18 guests have attended.

Step-by-step explanation:

To evaluate (f ∙ g)(18), we need to substitute 18 into both functions f(x) and g(x). First, substitute 18 into the function f(x) = 20 + 5x:

f(18) = 20 + 5(18) = 20 + 90 = 110

Next, substitute 18 into the function g(x) = 100 - x:

g(18) = 100 - 18 = 82

To evaluate (f ∙ g)(18), we multiply the values of f(18) and g(18):

(f ∙ g)(18) = 110 * 82 = 9020

In the context of the problem, (f ∙ g)(18) represents the cost per guest for an event where 18 guests have attended. The result, 9020, represents the total cost of catering for those 18 guests.

Answer 2

430 is the cost of catering 18 less than 100 guests.

Step-by-step explanation:

f(g(18))=f(100-18)=f(82)=20+5*82=430