Question

An arcade manager finds that revenue, R, based on a per-game fee, f, for unlimited play can be modeled by the function R=−480f2+3,120f . Which of the following correctly interprets the average rate of change in revenue if the per-game fee increased from $1 to $3?(1 point) Responses The per-game fee would decrease by an average of $1,200 per $1 increase in the revenue. The per-game fee would decrease by an average of $1,200 per $1 increase in the revenue. Revenue would increase by an average of $1,200 per $1 increase in the per-game fee. Revenue would increase by an average of $1,200 per $1 increase in the per-game fee. Revenue would decrease by an average of $1,200 per $1 increase in the per-game fee. Revenue would decrease by an average of $1,200 per $1 increase in the per-game fee. The per-game fee would increase by an average of $1,200 per $1 increase in the revenue. The per-game fee would increase by an average of $1,200 per $1 increase in the revenue.

Answer 1

To find the average rate of change in revenue when the per-game fee increases from $1 to $3, we first need to evaluate the revenue function \( R = -480f^2 + 3,120f \) at these two values of \( f \).

1. Calculate Revenue at \( f = 1 \):

   \[ R(1) = -480(1)^2 + 3,120(1) = -480 + 3,120 = 2,640 \]

2. Calculate Revenue at \( f = 3 \):

   \[ R(3) = -480(3)^2 + 3,120(3) = -480(9) + 3,120(3) = -4,320 + 9,360 = 5,040 \]

3. Average Rate of Change in Revenue from \( f = 1 \) to \( f = 3 \):

   \[ \text{Average Rate of Change} = \frac{R(3) - R(1)}{3 - 1} = \frac{5,040 - 2,640}{2} = \frac{2,400}{2} = 1,200 \]

This indicates that when the per-game fee increases from $1 to $3, the revenue increases by an average of $1,200 per $1 increase in the per-game fee.

Therefore, the correct interpretation is:

Revenue would increase by an average of $1,200 per $1 increase in the per-game fee.