One problem with 10 colonists is you do not have a very deep bench. If a couple of them croak you may not have enough people left to continue farming. Consider Jamestown, one of the early American colonies.
The following winter, disaster once again struck Jamestown. Only 60 of
500 colonists survived the period, now known as “the starving time.”
Historians have never determined exactly why so many perished,
although disease, famine (spurred by the worst drought in 800 years,
as climate records indicate), and Indian attacks took their toll. On
June 7, 1610, Jamestown’s residents abandoned the hapless town, but
the next day their ships were met by a convoy led by the new governor
of Virginia, Thomas West, Lord De La Ware, who ordered the settlers
back to the colony.
That is 88% mortality, which would leave 1.2 of your colonists alive. I bet the 0.2 guy would not be great company either. Unless your tech could keep his head alive in a jar, in which case he could tell jokes.
Where was I? Your colony's mortality rate will depend on the circumstances of your colony. Jamestown suffered from cold weather and famine. The missing colonists at Roanoake were probably killed by natives. Disease can be a factor. 10 people with advanced tech can work a farm and sidestep disease but if you lose some people, you may come to a tipping point where even with tractors you cannot produce your own food anymore.
In the short term the size of your colony will depend on how much food your colonists can produce for themselves (which depends on your environment, climate, crops and tech level) and causes for mortality / mortality rate. Jamestown seems pretty miserable. But if you are a boatload of shipwrecked slaves in the tropical Caicos, with no disease and the natives long gone, you can probably live off the ocean and your gardens very nicely.
The other issue with a colony is reproduction and sustainability over generations. This will be tricky in the short term with 10 adults. Colony implies self-sustaining, which means a birthrate and babies and kids. Someone has got to bear these kids and someone has got to keep these kids from falling down wells. You need kids if your colony is not going to die with the original colonists but child care (and no old folks or older kids to do it) will cut into your workforce as well.
The real long term deal killer for your 10 colonists colony: your gene pool is too small. When these kids grow up and have kids, who with? With 10 starting colonists, everyone in the colony will be related within a few generations. You are going to have serious inbreeding problems. If this is science fiction you could assert that these colonists have been made genetically pure, or perhaps there is a vat of frozen sperm to use which artificially increases the size of the gene pool. But if it is just 10 ordinary people their descendants are going to struggle.