Answer: It would take approximately 5730 years for 200 grams of carbon -14 to decay to 140 grams.
Explanation: Lets breakdown this into two parts.
Calculate the ratio of the final amount to the initial amounts:
final amount/initial amount
=140 grams/200 grams
=0.7
Determine the no. of half lives req to reach this ratio:
log(base1/2)(1/2)^(no. of half lives)= log (base 1/2 ) (0.7)
Number of half lives = log (base 1/2)(0.7)
= 0.5146
So, half life cannot be fraction. Therefore, it will take one half life for 200 grams of carbon -14 to decay to approximate 140 grams.
so it will take 5730 years to decay 140 grams.