Let's solve the problem with the corrected formula for $p$.

Given:

• $z = \text{Bullets fired}$ (values from 100 to 300 in multiples of 20)

The formula for total damage $p$ is: $p = \left( (0.5 \cdot z - 9) \times 122.5 \right) + 2025$

We will calculate $\frac{p}{z}$ for $z$ ranging from 100 to 300 in multiples of 20, and then calculate the percentage increase between successive values.

Calculations

For $z = 100$:

$p = \left( (0.5 \cdot 100 - 9) \times 122.5 \right) + 2025$ $p = \left( (50 - 9) \times 122.5 \right) + 2025$ $p = (41 \times 122.5) + 2025$ $p = 5022.5 + 2025$ $p = 7047.5$ $\frac{p}{z} = \frac{7047.5}{100} = 70.475$

For $z = 120$:

$p = \left( (0.5 \cdot 120 - 9) \times 122.5 \right) + 2025$ $p = \left( (60 - 9) \times 122.5 \right) + 2025$ $p = (51 \times 122.5) + 2025$ $p = 6247.5 + 2025$ $p = 8272.5$ $\frac{p}{z} = \frac{8272.5}{120} \approx 68.9375$

For $z = 140$:

$p = \left( (0.5 \cdot 140 - 9) \times 122.5 \right) + 2025$ $p = \left( (70 - 9) \times 122.5 \right) + 2025$ $p = (61 \times 122.5) + 2025$ $p = 7472.5 + 2025$ $p = 9497.5$ $\frac{p}{z} = \frac{9497.5}{140} \approx 67.8375$

For $z = 160$:

$p = \left( (0.5 \cdot 160 - 9) \times 122.5 \right) + 2025$ $p = \left( (80 - 9) \times 122.5 \right) + 2025$ $p = (71 \times 122.5) + 2025$ $p = 8697.5 + 2025$ $p = 10722.5$ $\frac{p}{z} = \frac{10722.5}{160} \approx 67.015625$

For $z = 180$:

$p = \left( (0.5 \cdot 180 - 9) \times 122.5 \right) + 2025$ $p = \left( (90 - 9) \times 122.5 \right) + 2025$ $p = (81 \times 122.5) + 2025$ $p = 9922.5 + 2025$ $p = 11947.5$ $\frac{p}{z} = \frac{11947.5}{180} \approx 66.375$

For $z = 200$:

$p = \left( (0.5 \cdot 200 - 9) \times 122.5 \right) + 2025$ $p = \left( (100 - 9) \times 122.5 \right) + 2025$ $p = (91 \times 122.5) + 2025$ $p = 11147.5 + 2025$ $p = 13172.5$ [ \frac{p}{z} = \frac{13172.5}{200