A first-order low-pass transmits most of a below-cutoff squared budget. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The signal is below the cutoff
The same 6 hertz signal compared to a 12 hertz cutoff has index 1/2.
x=21
The low-pass squared ratio is four fifths
The low-pass ratio is 4/5, so budget 20 becomes 16.