Check my math!

Hey, I was hoping some more experienced players could give me some feedback on this exercise spoony gave me:

Here is the scenario:

• Hero raises pre-flop from early position with AK to $0.08 (playing 2NL).
• A tight-aggressive player on the button calls and everyone else folds.
• The flop comes Qs9h5c and the flop pot is $0.19.
• I want to figure out if a continuation bet of $0.14 is going to be profitable.

My raise would be 0.14 into a 0.19 pot, so: 0.14/(0.14+0.19) = 33%
I need the villain to fold more than 33% of the time for the bluff to be profitable.

I have come up with an arbitrary range for the villain. I see all sorts in 2NL so I don't think this is too unrealistic...

Villain Preflop range: 99+,ATs+,KJs+,QJs,AJo+,KJo+,QJo
Meaning that (taking into account that I hold AK) he has 118/1176 combos that he calls with = 10.03%

Villain Postflop range (in response to my raise): QQ+,99,AQs,KQs,QJs,AQo,KQo,QJo
54/1176 combos = 4.59%

So villain is folding 54/118 to my raise = 46% of the time. 46 > 33, so the bluff is profitable.

Criticism would be much appreciated! Cheers big ears