Question

Wang Xiu Ying is gift wrapping boxes in the shape of a cube for her class fundraiser. She calculates that the surface area, S SS, in square feet, of a cube-shaped box with a side of m mm feet is given by the function S ( m ) = 6 m 2 S(m)=6m 2 S, left parenthesis, m, right parenthesis, equals, 6, m, squared. She also finds that the cost, C CC, in dollars, of wrapping a box with a surface area of x xx square feet is given by the function C ( x ) = 0.15 x + 0.25 C(x)=0.15x+0.25C, left parenthesis, x, right parenthesis, equals, 0, point, 15, x, plus, 0, point, 25. Find an explicit expression that models the costs of wrapping a cube shaped box with a side length of m mm feet.

Answer 1

Answer:

$C(m)=0.9m^2+0.25$

Step-by-step explanation:

The surface area of a cube-shaped box with a side of m feet is given by the function:

$S(m)=6m^2$

The cost, C, in dollars, of wrapping a box with a surface area of x square feet is given by the function:

$C ( x ) = 0.15 x + 0.25$

We want to find an explicit expression that models the costs of wrapping a cube-shaped box with a side length of m feet.

In the cost function, C(x), x is the surface area, therefore:

$S(m)=x; and \\C ( S(m) ) = 0.15(6m^2) + 0.25\\C(m)=0.9m^2+0.25$

To find the cost of wrapping a cube of side length m feet, we use the explicit function:

$C(m)=0.9m^2+0.25$