The yearly cost in dollars, y, at a video game arcade based on total game tokens purchased, x, is y = y equals StartFraction 1 Over 10 EndFraction x plus 60.x + 60 for a member and y = y equals StartFraction 1 Over 5 EndFraction x. x for a nonmember. Explain how the graph of a nonmember’s yearly cost will differ from the graph of a member’s yearly cost.

Question

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Answer 1

The graph of a nonmember's yearly cost will differ from the graph of a member's yearly cost in two main ways.

Firstly, the slope of the nonmember's cost function is steeper than the slope of the member's cost function. This means that for each additional game token purchased, the cost for a nonmember will increase at a faster rate compared to the cost for a member.

Secondly, the nonmember's cost function does not have a constant term (60) like the member's cost function does. This means that the nonmember's cost function will intersect the y-axis at the origin (0,0) unlike the member's cost function which will intersect the y-axis at (0,60). This indicates that even if no game tokens are purchased, a member will still incur a yearly cost of $60 while a nonmember will not have any cost.

Overall, the graph of a nonmember's yearly cost will have a steeper slope and will not have a constant term, leading to a different shape and starting point compared to the graph of a member's yearly cost.