How much food does it take to get a dragon to level 15?

I want to raise some dragons to level 15 as it's the highest level I can reach.

How many treats (total) does it take to get a dragon from level 1 to 15?

Hooray math time!

Dragons start off at level 1, needing to be fed 5 units of food at a time. Every level after that, the amount of food doubles - level 2 requires 10 food, level 3 requires 20 food, etc. You need to feed a dragon four times before it levels, so we can factor that in and pretend it's already required - a level 1 dragon requires 5 * 4 = 20 units of food to level, a level 2 dragon requires 40, a level 3 dragon requires 80, and so on.

Now, if we factor out 20 units of food from those numbers (it's 5 * 4, which are just constants we've applied), we get a simple pattern: level 1 requires 1, level 2 requires 2, level 3 requires 4, level 4 requires 8, and so on; if we can figure out a quick way to sum that up from level 1 to level 15, (or alternatively, from 2^0 to 2^14) then we just need to multiply everything by 20 and we'll have our answer.

Since we need to take the sum of those things, and we can tell by looking at them that they're powers of two, we stick "sum of powers of 2" into the ALL KNOWING ORACLE. That gives us this result, where someone says that the formula is 2^(N+1)-1 and that this is in fact a geometric series, and then we lose like three hours on Wikipedia but that's okay.

So, now we know that the equation is going to be of the form 20 * (2^(N+1)-1) or maybe it's N-1 or maybe just N, I don't know, I kinda lost track during that Wikipedia binge. Since it's early in the morning and we're not entirely sure we did that right, we'll write down the values that 20 * (2^(N)-1) puts out and see how they match what we know:

N: Result
1: 20
2: 60
3: 140

So it looks like if you want to do this calculation for level N, you'd put in N-1, making it 20 * (2^(N-1)-1). Otherwise, the values look good. Yay!

tl;dr:

It requires 327660 units of food to take a dragon from level 1 to the beginning of level 15, or 655340 units of food to take the dragon to the end of level 15 (a full food bar). In general, you can calculate the amount of food required to take a dragon from level 1 to level N by plugging N into the equation 20 * (2^(N-1)-1).

The amount of treats required per level starts at 20 for level 1 and doubles every level. Per the DragonVale Wiki this means that by level 15 you will require 163,840 treats to go from level 14 to level 15. To your exact question, that means the cumulative total you'll need to go from level 1 to level 15 is 327,660 treats.

I have played this for a looong time and I noticed it takes roughly 10,000 food to get a dragon to level 10 and then if i have at least 320,000 food or something close to that then I can easily get it to level 15 with food left over