Question

The total number of fans who went to watch professional soccer games in the last decade can be modeled by the function f(x)=x3+9x2+23x+15 and the number of professional soccer games played in this time period can be modeled by g(x)=x+5 , where x is the number of years.Write an expression, h(x) , in standard form that describes the average number of fans per soccer game.

Answer 1

The average number of fans per soccer game, h(x), is expressed as the division of the total number of fans function f(x) by the total number of games function g(x), resulting in h(x) = (x^3 + 9x^2 + 23x + 15)/(x + 5).

Step-by-step explanation:

The question asks for an expression, h(x), that describes the average number of fans per soccer game over the last decade. Given the total number of fans who went to watch professional soccer games is modeled by f(x) = x3 + 9x2 + 23x + 15 and the number of professional soccer games played is modeled by g(x) = x + 5, we can find h(x) by dividing f(x) by g(x).

First, write the expression for the average number of fans per game:

h(x) = f(x)/g(x)

Inserting the functions for f(x) and g(x):

h(x) = (x3 + 9x2 + 23x + 15)/(x + 5)

Therefore, h(x) is the required expression representing the average number of fans per game in standard form, which is found by dividing the function that represents the total number of fans by the function that represents the total number of games.