A low-pass filter is to be designed to pass frequencies in the 0 to \(12 \mathrm{kHz}\) range. The gain of the amplifier is to be +10 at the low frequency and change by no more than 10 percent over the frequency range. In addition, the gain of the amplifier for frequencies greater than \(14 \mathrm{kHz}\) is to be no greater than 0.1 . Determine \(f_{3-\mathrm{dB}}\) and the number of poles required in a Butterworth filter.