To find the average rate of change in revenue, \( R \), when the per-game fee, \( f \), increases from $1 to $3, we can evaluate the function \( R = -480f^2 + 3120f \) at these two points.
- First, calculate \( R \) at \( f = 1 \):
\[ R(1) = -480(1^2) + 3120(1) = -480 + 3120 = 2640 \]
- Next, calculate \( R \) at \( f = 3 \):
\[ R(3) = -480(3^2) + 3120(3) = -480(9) + 9360 = -4320 + 9360 = 5040 \]
- Now, calculate the change in revenue as the fee changes from $1 to $3:
\[ \Delta R = R(3) - R(1) = 5040 - 2640 = 2400 \]
- The change in the per-game fee is:
\[ \Delta f = 3 - 1 = 2 \]
- The average rate of change in revenue per $1 increase in the per-game fee can be found by dividing the change in revenue by the change in the per-game fee. Since the change in the fee is $2, the average increase in revenue per $1 increase in fee is:
\[ \text{Average rate of change} = \frac{\Delta R}{\Delta f} = \frac{2400}{2} = 1200 \]
Thus, the average rate of change in revenue is $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.