Is dark reaction autotrophic or heterotrophic

Autotrophic.

Dark reaction happens in the photosynthetic process of plants or autotrophs.
(a) A giant redwood tree = Autotroph
(b) A spider = Heterotroph
(c) A rose bush = Autotroph
(d) A mushroom = Heterotroph
(e) A blue whale = Heterotroph
Autrophs are the organisms that have the capacity to form their own food from inorganic substances like the carbon dioxide. 
Heterotrophs are the organisms that cannot produce their own food but depends on other animals or plants for their nutritional needs.

answer: carbon 14 can only be used to determine the age of the organisms that were once living, and igneous rocks are non living.

explanation:

carbon 14 dating is used to determine the age of the sample by estimating the amount of carbon 14 present in the sample and then comparing it with a reference standard.carbon 14 is a isotope of carbon which is radioactive and unstable. carbon 14 is assimilated by all plants and animals throughout their life from carbon dioxide. however, one the organisms die they stop this assimilation and the carbon 14 content starts to decrease.by knowing how much of carbon 14 is left in an organism after his death, one can estimate the age of the organism. the materials whose age can be estimated by carbon 14 method are the organic compounds. however, some inorganic compounds such as aragonite   shell can also be dated.however, if we consider the igneous rocks it is a non living component which never accumulated carbon 14 in it and thus, we cannot use carbon 14 dating method to estimate its age.