Step 1: Take logs of the affinity law.
Since $P \propto N^3$, the ratio of powers satisfies $\ln n = 3 \ln\left(\dfrac{N_2}{N_1}\right)$.
Step 2: Insert the speed increase.
Here $\dfrac{N_2}{N_1} = 1.30$, and $\ln(1.30) = 0.2624$.
$\ln n = 3 \times 0.2624 = 0.7871$.
Step 3: Undo the logarithm.
$n = e^{0.7871} = 2.197$.
Final Answer:
This confirms the power goes up by close to 2.20 times, agreeing with the direct cube calculation.
\[ \boxed{n \approx 2.20} \]