My family thinks the world is 10,000 years old! So i wrote them this

you cannot argue science with a person of "great faith" which is extremely frustrating.................................................

I am often exposed to this kind of mentality, and have taken note time and time again that arguing with science and math has no impact on the potent will of a creationist. Interestingly enough, creationists are by no means backed into a corner in terms of their entire religion going bust but seem to fear that almost as much as god himself. If a compromise of thought were to occur, and we could accept that maybe some terminology in religious texts is more of an analogy, and that the writers perceived many things differently as we do today, creationism would make a lot more sense.

The scientific community is rather unanimous millions of topics; from how cellphones work to the orbit patterns of the earth we have got this shit figured out. These sciences have advanced far beyond theory and have been proven not only through scientific development, but through use in our everyday lives and by observation. These are in my opinion the 3 most definitive, clearly observed reasons the earth is older than 10,000 years.

1. Ice cores -----
   
   Above is a well preserved ice core, with clear annual rings separated by ice and snow layers (summer and winter layers). Scientists have taken core samples with over 700,000 years worth of layers!

2. Lack of DNA in fossils -----
   
   DNA is very durable, and takes a incredibly long time to degrade. With all dinosaur fossils we have found, none of them have intact DNA, which is solid evidence that they have been in the ground for millions of years. (not to mention carbon dating and many more accurate dating methods which have been proven by dating objects of known age time and time again)

3. Permafrost -----
   
   Permafrost (frozen ground) is a slow process. Because earth is a good insulator and permafrost forms downward from the surface. In the Prudhoe Bay oil fields of Alaska, the permafrost extends over 600 meters into the ground, requiring at least 200,000 years even at ice age temperatures.

4. Coral -----
   
   Corals are marine organisms that slowly grow on top of each other, over time forming reefs. This process of growth and extremely slow, and some of the larger reefs have been "growing" for hundreds of thousands of years. The Great Barrier Reef Marine Park Authority estimates that corals have been growing on the Great Barrier Reef for 25 million years, and that coral reef structures have existed on the Great Barrier Reef for at least 600,000 years.

5. Tree rings -----
   
   The oldest living tree is over 5,000 years old! and has clearly definable rings of growth for each year, making Methuselah half the age of earth itself!

6. The solar system -----
   
   for millions of years our planets have orbited the sun, along the way creating a unique road map to where they have been, a map that can be traced back in time, much like the path of ball on a billiards table.

There are literally thousands of other ways to confirm age of objects that have formed an interconnected system that has been proven beyond theory. If you are willing as a person to accept the science behind a cellphone, which requires literally slinging a rocket around the earth... you should be able to accept these simple truths. Good luck out there!