At the very beginning of the human race, God commanded Adam and Eve to take care of the world and not spoil it or misuse it: "The Lord God took the man and put him in the Garden of Eden to work it and take care of it" (Genesis 2:15). That mandate is still in force, and we must take it seriously.
The Bible also teaches, however, that someday the world as we know it will come to an end. But this won't happen because of any human action - but because of God's intervention. Someday, God will bring an end to the present world system, and Christ will come again to establish His kingdom of perfect righteousness and justice. And at the end of time the whole creation will be made new. The last book of the Bible puts it this way: "Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away" (Revelation 21:1).
Does this mean we shouldn't bother taking care of the world, since it will come to an end anyway? No, not at all. Jesus reached out to the hungry and hurting - and so must we. He commands us to alleviate suffering and work for a better world in the name of Christ.
At the same time, don't be paralyzed by fears of the future. The future is in God's hands - and so are we. Have you committed your life - and your future - to Christ?