What does carrying capacity refer to?
the ability of a community to welcome new immigrants
the capacity for globalism within a given ethnic group
the amount of life that can be supported sustainably in a particular environment
the amount of weight that urban centers can bear if vertical growth is mandated

 the correct answer is the amount of life that can be supported sustainably in a particular environment .

d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."