In my world, approximately 100 humans with were stranded on a planet with nothing but the clothes on their backs. They all have at least high school education, but most of them do not have degrees. How far would technology have progressed for them in that time, if none of them died in that time?
How far would technology have progressed for them in that time
I think you mean "from zero, which is what they started from".
It almost completely depends on the planet. First thing they're going to do is find food and shelter. Resources shall have to be dedicated to this. How much, it depends on how easy it is to find food.
They will start as hunters-gatherers, and try to reach the agricultural stage, but this will take optimistically no less than three or four years (they need to identify edible plants first, even if someone knows the testing drill or reproduces it accidentally or as an alternative to starvation).
Then comes animal husbandry, and this might be well under way around the ten-years mark. If everything goes exceedingly well, or they have large strokes of luck. For example they can disrupt some predator/prey relationship and establish themselves as new, and more "illuminated", predators - not just eating prey but caring for it until it's dinner time. Being able to gather fodder for prey animals without worrying about predators might allow a quick growth of the captive prey population.
Meanwhile it's rediscovery of fire, and looking for metal deposits. With no technology to start with, you need to find tin and copper to at least smelt bronze, but to do so you need to know what tin and copper deposits look like. And of course there must be such deposits within reach.
I don't expect your hundred guys - possibly as many as one hundred and twenty by now, and boy does this add to problems - to have progressed much farther past the knapped flint stage.
All this completely abstracts from a whole different lot of problems, i.e. how they will take this psychologically and what long game they're going to decide to play ("wait for rescue" or "be fruitful and multiply", in which case some way of preserving their culture and as-yet-useless knowledge must be found before the first generation is dead by old age - and, now, with no medicines or therapies or technology, not even to replace a pair of glasses, "old age" comes much earlier)
Depends on the story you want to tell. One realistic option is that they all die of starvation, which you have excluded.
- No technology beyond the stone age, but certain bits of knowledge like germ theory or Mendelian genetics.
- Stone age plus, no metalworking but many "practical tricks" like pulleys, wooden wheelbarrows, keystone arches, and crop rotation.
- Even simple metalworking is probably improbable. First they have to find the ore, then they have to invent charcoal production, then they have to invent smelters ...
Knowledge has come to a point where it is needed hundreds of universities just to transfer it to the next generations, and yet we find people believing - and preaching - that the Earth is flat!
Even if your 100 people group is composed by scientists of diversified fields, they can't possibly hold all the current knowledge/technology, let alone high-school educated people. Thus, in 15 years the humans in your planet would probably be living in a 1800s-like society.
You are already postulating a ridiculously unlikely scenario with the stipulation of
if none of them died in that time
As that is by far the most likely outcome.
SO we have to assume an environment where there is a very benign, controlled environment. Food and medical needs are "somehow" provided for.
Under that requirement: As the guy shows us in Youtube channel Primitive Technology, it is quite easy to settle into a reasonably advanced stoneage settlement, with good buildings, agriculture (but crop plants&seedstock may be an issue), pottery. The people will know about domestication of animals, unfortunately the chance of finding a suitably pre-domesticted animal are very low, and any systematic project of domestication is easy but will require many generations of the animal. Thus in 15 years, I expect not much more than forcibly-caged chicken analogues, at best.
With access to copper deposits, smelting copper is reasonably easy. Same for adding tin and making bronze, although it is much easier to identify copper deposits than bronze.
Access to Iron Ore is very common, but actually managing to smelt iron is likely to be beyond your 100-person's collective knowledge. It is hard to smelt iron without having previous experience of doing so, and even with the right skills it is a specialized job. Still, assume they manage to make iron, and primitive forged tools.
Reading/writing, of course. Paper may be a problem, and parchment is right out due to lack of domestic animals. But tablets, bark, etc. should be easily accessible. Likely one of your 100 will know how to make Papyrus and suitable pigments for Ink.
Water engineering. Dams, lesser aqueducts, running (cold) water. Waste disposal.
Basic agriculture, severely hampered by the absence of seedstock of the over-time-genetically-engineered plants we are used to, like fruittrees, wheat, corn, tomatoes, carrots,.... actually I would be surprised if any of your 100 have every eaten a cultivated plant that occurs in original form in nature, not the result of many generations of selective cultivation.
Basic animal husbandry, again severely hampered by the lack of breeding stock of pre-domesticated animals.
Pottery. This means clay vessels or bricks or even tools, that are then fired. This requires pottery knowledge, which is reasonably common, and also charcoal which is easy to make but not many people know how to. Still, expect some of your team to know the process.
Metalwork. Once you have charcoal, and pottery skills, you can smelt and shape copper easily. The ore is very easy to identify, although a bit rare. Iron may be possible, but is a much harder task.
Medical. Your people will be skilled in basic first aid, they will know about germ theory and chemical medicines but will be utterly unable to do anything about it! Especially under the stipulation "do not have degrees". But even a fully qualified and experienced modern surgeon will be marginally effective at best, with zero access to his tools and drugs. So sorry, but your medical treatment is likely to be at "skilled boy scout" level, only. As per scenario stipulation above, there will need to be some form of intervention for your people to survive their inevitable malnourishment, broken bones, and the diseases they brought along with themselves. Not to mention animal attacks, internecine fighting, and mental freakouts tat are likely to occur.
Electricity. There is no realistic timeframe for the development and use of Electricity in any form. They have the time and skills to putter around with it, but not to make any useful device, as that requires levels of metallurgy and tooling that will be far beyond them.
Mechanisms. Similarly, while everyone will KNOW about wheels and bearings and such, do not expect anything better than a hand-drawn cart or wheelbarrow to make an appearance. The lack of good metal for bearings, and of draft animals for pulling, makes wagons etc. impractical. Most complex mechanism would be a waterwheel or similar.
They would not advance at all
I'm taking you at your word that they have nothing but the clothes on their backs.
They would be entirely focused on survival for the first 3-5 years. Growing food, building shelter, protecting themselves against any predators, etc. They'd be focusing on medieval-era technology to do this as it utilizes naturally-available resources without industrial technology better. So, up to a third of the time is lost just getting to the point of thinking about something new.
All of today's technology depends on a massive (massive) industrial infrastructure that would be needed to create a new technology in any science other than mathematics. They couldn't even hope to begin re-creating that infrastructure (buildings, machines, utilities, etc....) in a 10 or 15 year period. Not from scratch. Consider my answers to the following questions: , , , . Keep in mind that your question is fundamentally a duplicate of any or all of those questions.
Conclusion: As I wrote my answer, it's theoretically possible that an advance could be made in mathematics because all you need for that is a writing instrument and something on which to write that would last for a year or two. But even that's impractical to believe since developing a durable media for storing knowledge using symbology more precise than hieroglyphics is no simple task. So I'm sticking with they'd make no advance at all.