Each change by k% multiplies price by:

• Increase by k% → factor = $\frac{(100 + k)}{100}$
• Decrease by k% → factor = $\frac{(100 - k)}{100}$

Over four steps (↑k, ↓k, ↑k, ↓k): q = p × $[\frac{(100 + k)}{100} × \frac{(100 - k)}{100}]^2$ = p × $[\frac{(10000 - k^2)}{10000}]^2$ = p × $\frac{(10000 - k^2)^2}{10^8}$

Rearranging: q × $10^8$ = p × $(10^4 - k^2)^2$ ⇒ p$(10^4 - k^2)^2$ = q × $10^8$