The halflife of Carbon14 is about 5700 years You have found

The half-life of Carbon-14 is about 5700 years. You have found a fossil that you believe to be about 34,200 years old because it has _____ the normal (modern) expected ratio of Carbon-14C

Solution

Important to understand the concept of half life.

If \'x\' amount of Carbon-14 is available today and its half life is 5700 years - it means after 5700 years \'x/2\' of Carbon-14 will only be available and the remaining will decay.

Accordingly - 1/4th original will remain after (5700*2) years.

Therefore - 34,200/5700 = 6

So, the denominator will have - 2^6 (2 power 6) = 1/64 times the morden ratio of Carbon-14.

Hope this helps.