Carbon-14 has a half-life of 5370 years. This means that

after 5370 years half of the atoms have decayed.

How many years will it take for a quantity of carbon-14

to become 1/8 of its original size?

a quantity of carbon - 14 will take 1342.5 years to become 1/8 of its original size.

Step-by-step explanation:

1/2 of the atoms decayed after 5370 years

now half of (1/2 of) the atoms decayed after 5370 / 2 years

i. e, 1/4 of the atoms decayed after 2685 years.

again half of (1/4 of the atoms) decayed after 2685/2 years

i. e, 1/8 of the atoms decayed after 1342.5 years.