Question

The half-life of carbon 14, which is commonly used to date organic materials, is 5700 years. What is the minimum age of sample in which less than 1% of the organic carbon 14 is left?

Answer 1

If 1% is left,
(0.01) = (0.5)^N
where N is the number of half-lives.

N = 6.644
minimum age = 37,900 years

There will be less than 1% left if the sample is older than that, so that is a minimum age.

There is not much about astronomy here

Answer 2

Find the age for a rock for which you determine that 68% of the original uranium-238 remains, while the other 32% has decayed into lead.