In "classic" cameras systems exposures varied by a factor of two between adjustment steps and by a factor of 2 with standard aperture number changes. The aperture f numbers usually provided vary by a factor of square root of 2 as the aperture is proportional to the square of the diameter and stop numbers relate to the diameter.
ie aperture is an area measure which is proportional to diameter squared. Yes, that hopefully makes sense if you read it slowly a few times :-).

The important thing is that a "classic" range of exposure times would be, starting at 1 second:

• 1 2 4 8 16 32 64 128 ...

The question is more why it would be labelled 15.

They may well be wanting to match the times to fractions of a minute so eg

• 1 2 4 8 15 30 60 120 ...

BUT leaving theactual values in a true power of 2 progression from 1 second.

However, going to faster steps starting at 1 second we also "run into problems".

1 1/2 1/4 1/8 1/16 1/32 1/64 1/128 is OK in fractional form BUT when written as decimal we get

1 0.5 0.25 0.125 0.0625 0.03125 0.015... ... you get the idea. Gets messy.

SO along the way people cheated slightly. The series may end up slightly like

1 1/2 1/4 1/8 1/16 1/30 1/60 1/125 1/250 1/500 1/1000 1/2000 1/4000 1/8000 ...

The decimal values get untidy around 1/16th to 1/125th but get tidy again below 1.250th and people largely don't use these.

The slight errors introduced are inside the margin of error in all but the most tightly controlled lighting situations and well inside what any eye-brain can guarantee they have seen (even if the eye can actually resolve it).

The first few differences are:

1/32 : 1/30 = 6.7% longer 1/64 : 1/60 = +6.6% longer 1/128 : 1/125 = +2.4% 1/256 : 1/250 = +2.4% at all settings above here

Your 15 seconds shown, 16 seconds actual is 6.7% longer than shown.

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BUT many modern cameras blow all this away with shutter speeds in 0.3 EV or other steps that seem good to them. Worse, auto ISO or shutter speed or aperture systems may choose semi random settings so you MAY see eg 1/325th of a second. Very hard on classical system sensibilities ;-).