Generally, it takes 10x the power, for 2x the loudness. So, it takes 10 watts to go twice as loud as a 1 watt, and 100 watts to go twice as loud as a 10 watt. (Assuming equivalent speaker efficiency's.)
Also, the RMS = continuous power is a bit of a misnomer. RMS has nothing to do with continuous output power. Used in this context, its a marketing term left over from the 70's and 80's audio specs. Manufacturers used it, mistakenly, to refer to the continuous power output of their amps.
RMS
does, in fact, stand for "root/mean/squared", but its a technique for calculating the average power of a AC signal, made up of combination of different frequencies. But it doesn't mean "continuous power". FYI