Care for the environment will become very important as earth

care 可以作动词,但是也直接可以作名词.这里就是名词.
句子成分划分可以帮助理
【Care主语】【 for the environment主语的定语】 【will become 谓语】【very important表语 】【as earth's matural resources run out.原因状语从句】.
care
[kZE]
n.
注意,小心
照料,关心,护理
挂念; 忧虑; 忧愁
[常用复]心事
care of tools
爱护工具
care of the children
照管孩子
Take care that no mistakes be made.
当心不要出错.
Few people are free from care.
很少人是无忧无虑的.
C-has made her look ten years older.
忧愁使她看起来老了十年.
care
[kZE]
vi.
关心
喜欢; 爱好
照顾
I don't care for music.
我不爱好音乐.
He cares for no one.
他不顾别人.
care
[kZE]
vt.
[方]照顾,关心
[方]介意,计较,愿意
Nobody cares what I do.
没有人管我干什么.
I don't care how far I'll have to go.
无论走多远,我都不在乎.
努力吧,你的好学、多思的习惯会让你成为了不起的人!
祝你开心如意!

支持你，用caring！要敢于挑战权威。

因为这里的care是名词

care 是名词，caring是动名词，他们都可以做主语。动名词强调动作。这个句子不是强调动作，而是状态，所以，名词做主语更合适些