$($Problem $4$: $10\%)$

Given a $1k$ resistor, what size capacitor would be required to build a single pole Butterworth low pass filter with a cut off frequency of $100$ Hz $?$

$($a$)1\mathrm{.}59F$

$($b$)5F$

$($c$)2\mathrm{.}5F$

$($d$)100F$