Question

An empty gasoline container weighs 1.75 pounds. It is filled with gasoline that weighs 6.28 pounds per gallon. Which of the following functions properly models the total weight of the container and gasoline, w, as a function of the number of gallons of gasoline it holds, g?

1) w = 1.75 + 6.28g
2) w = 1.75 - 6.28g
3) w = 1.75 * 6.28g
4) w = 1.75 / 6.28g

Answer 1

The total weight of the container and gasoline as a function of the number of gallons is modeled by the linear equation w = 1.75 + 6.28g, representing the initial weight of the container plus the weight of the gasoline per gallon.

Step-by-step explanation:

The student is tasked with identifying the function that models the total weight of a container and gasoline, w, as a function of the number of gallons of gasoline, g. The model is a linear relationship because each gallon of gasoline adds a constant amount of weight to the total. Therefore, the function that represents this relationship is:

w = 1.75 + 6.28g

This equation makes sense because when g (the number of gallons of gasoline) is 0, the weight w is just the weight of the empty container, which is 1.75 pounds. For each additional gallon of gasoline, 6.28 pounds are added to this initial weight. Thus, Option 1 is the correct answer:

w = 1.75 + 6.28g