Question

The contractor installing a new field has developed two functions to model costs associated with its installation. Function f models the cost, in dollars, to fence in a rectangular field with an area of x square meters: f(x)=5x+300. Function g models the cost, in dollars, to lay new grass on a rectangular field with an area of x square meters: g(x)=20x+600.

Function c models the total cost, in dollars, to lay new grass and fence in the new rectangular practice field with an area of x square meters. Which is function c?
a. c(x)=100x²+180,000
b. c(x)=100x+180,000
c. c(x)=25x²+900
d. c(x)=25x+900

Answer 1

The total cost function c(x) for installing a new field is obtained by adding the fencing and grass laying cost functions f(x) and g(x). After simplifying, the total cost function is c(x)=25x+900. Option number d is correct.

Step-by-step explanation:

The question is asking for the function c(x) that models the total cost, in dollars, to lay new grass and fence in a rectangular field with an area of x square meters. To find the total cost, you need to add the costs of fencing and laying new grass together.

The cost to fence in the field is modeled by the function f(x)=5x+300, and the cost to lay new grass is modeled by the function g(x)=20x+600. By adding these two functions together, we get:

c(x) = f(x) + g(x) = (5x + 300) + (20x + 600)

Simplifying the right side, we combine like terms:

c(x) = 5x + 20x + 300 + 600 = 25x + 900

Therefore, the function that models the total cost is c(x)=25x+900.