Not being entirely sure by what is meant by 'peaks increasing expotentially' and for the benefit of others facing a decision about how much power is needed, consider this as a rough guide.
Assuming you anticipate that the average sound pressure level of your music will have peaks 15db higher than the average SPL, not an unreasonable assumption, I think (nor is it absolute), if you are listening to pop, jazz, & classical music.
Assume your speakers have an efficiency of 86db's.
Assume you have a meduim sized room where I think an 85db SPL would be considered by most to be fairly loud but still within the ability of the room to respond without overloading. The following watts would be needed to producte the indicated SPL. This little chart contains no consideration of current needs, impedence values etc.
1 wt - 86db
2 wt - 89 db
4 4t - 92 db
8 wt - 95 db
16 wt - 98 db
32 wt - 101 db
64 wt - 104 db
128 wt - 107 db
256 wt - 110 db
512 wt - 113 db
1024 wt - 116 db
IF, and only IF, you found my 85db average SPL reasonable, and you add 15 db to that, you would only need 32wts. Now if you want 3 or even 6 dbs of headroom you would need no more that 60 or 120 wts (BTW all numbers are rough/rounded and meant for illustration).
FWIW.