Question

An arcade sells game cards that customers can use to play the arcade games. A game card

comes stocked with credits, and each game costs 5 credits to play. Shivani was able to play
16 games before her card ran out of credits.
Graph the function that models the relationship between the number of games Shivani
played, n, and the number of credits remaining on her card, C(n).
Select points on the graph to plot them.

Answer 1

To model the relationship between the number of games Shivani played and the remaining credits, we define a linear function C(n) = T - 5n. The graph is a straight line with a slope of -5 representing the constant rate of 5 credits per game and intercepting the vertical axis at the initial total credits. Plotting this function involves determining the number of remaining credits after each game played until the credits reach zero.

Step-by-step explanation:

The function that models the relationship between the number of games Shivani played, n, and the number of credits remaining on her card, C(n), can be expressed as C(n) = T - 5n, where T is the total number of credits on the card initially. Since Shivani played 16 games before her card ran out, she spent a total of 16 × 5 = 80 credits. To graph this function, we would plot the number of games on the horizontal axis and the remaining credits on the vertical axis.

For example, if Shivani starts with 80 credits, after 0 games, she would have 80 credits left - this is our starting point (0, 80). After 1 game, she would have 80 - (1 × 5) = 75 credits left, giving us the point (1, 75). We would continue this process to plot additional points, such as (2, 70), (3, 65), and so on until we reach (16, 0), which indicates she has no credits left.

To graph, we would connect these points to form a straight line showing the linear decrease in credits as the number of games increases. The slope of this line should be -5, indicating the rate at which credits are spent per game.

Answer 2

Answer: The function that models the relationship between the number of games played (n) and the number of credits remaining on the card (C(n)) is C(n) = 5n.

Step-by-step explanation: This function can be derived by realizing that each game costs 5 credits to play, so as the number of games played (n) increases, the number of credits remaining on the card (C(n)) decreases by 5 for each game played.

For example, if Shivani played 16 games before her card ran out of credits, we can substitute n = 16 into the function to find that C(16) = 5(16) = 80 credits. This means that her card had 80 credits on it before she started playing games.

To plot points on the graph, we can select a few different values of n and substitute them into the function to find the corresponding values of C(n). Here are a few examples:

When n = 0, C(n) = 5(0) = 0. This represents the case when Shivani has not played any games yet and has no remaining credits on her card.

When n = 8, C(n) = 5(8) = 40. This represents the case when Shivani has played 8 games and has 40 credits remaining on her card.

When n = 16, C(n) = 5(16) = 80. This represents the case when Shivani has played 16 games and her card has no remaining credits.

We can plot these points on the graph and label them (0,0), (8,40), (16,0) respectively.

Note that the y-intercept is (0,0) and the x-intercept is (16,0)

Graph:

n C(n)

0 0

8 40

16 0

The graph is a straight line starting from (0,0) and going down till (16,0) with a slope of -5.