Even pessimistically over one human lifetime I bet that "15 people" turns into at least 30.

You get gene pool and interbreeding issues with too small of a pool, then again you'd be amazed what you can store in liq nitrogen for a long time.

Also looking at the temporary and limited mineral and energy requirements, the earth isn't going to support 7B or 9B or even 1B for much longer, on a geologic / radiation timescale.

For awhile you can turn mined petrochemicals and chemical fertilizers into lots of human biomass. The key is for awhile, temporarily.