An enzyme is subject to allosteric regulation . how would you design an inhibitor of the enzyme that was competitive? non-competitive? irreversible?

Allosteric regulation or non-competitive is the same concept. Allosteric means, from the Greek, another place/other space.
So, starting by a non-competitive inhibitor, you could design an enzyme like a circle with two separate spots/recesses, symbolising connecting spots, one for the inhibitor and another one for the substrate. When the inhibitor is then placed into its position it changes the conformity of substrate's spot impeding it to connect.
For a competitive inhibitor, you could again design an enzyme like a circle but now only with a single binding spot where the inhibitor would connect so the substrate could not.
As for the irreversible inhibitor, you could design an enzyme as a circle again but it doesn't matter where you connect the inhibitor, whether on the substrate spot or not, as long as you make clear that there is a strong covalent bond between the enzyme and the inhibitor that doesn't allow the substrate to bind to the enzyme. You could represent this covalent bond by a simple trace connecting the enzyme to the inhibitor: -- .

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.