Question

James is playing his favorite game at the arcade. After playing the game 33 times, he has 88 tokens remaining. He initially had 2020 tokens, and the game costs the same number of tokens each time. The number tt of tokens James has is a function of gg, the number of games he plays

Answer 1

`t(g)=-4g+20`

Explanation:

Let g be the number of games James plays and t be the number of tokens James has.

We will write our function's formula in slope-intercept form of equation.

`y=mx+b`, where,

m = Slope of line,

b = y-intercept.

We have been given that initially James has 20 tokens. This means that before playing the games James has 20 tokens or at g equals 0 t equals 20. So our y-intercept will be 20.

We are also told that after playing the game 3 times, he has 8 tokens remaining.

Let us find the slope of line using points (3,8) and (0,20).

`m=(y_2-y_1)/(x_2-x_1)`, where,

m = Slope of line,

`y_2-y_1`= Difference between two y-coordinates,

`x_2-x_1`= Difference between x-coordinates of same two y-coordinates.

Upon substituting coordinates of our given points we will get,

`m=(8-20)/(3-0)`

`m=(-12)/(3)`

`m=-4`

So the slope of our line will be -4.

We can see that number of remaining tokens are dependent on number games James plays, this mean that t is a function of g.

Upon substituting our values in slope-intercept form of equation we will get,

`t(g)=-4g+20`, where, t(g) represents number of tokens James has left after playing g games.

Therefore, our required function will be
`t(g)=-4g+20`.