Here are some ideas I thought of and a few that I gleaned from a few references. You will need to find several others to complete this assignment.

Only some 150 square miles in area, Easter Island is a microcosm for the problems we face today. Its native inhabitants arrived in the fifth century AD and quickly established a highly advanced culture of about 7,000-15,000 people. By the 18th century, the few remaining islanders lived in a primative manner. The harsh conditions they faced are indicated in oral traditions which focus on cannibalism. To severely insult an enemy one would say: "The flesh of your mother sticks between my teeth" (Diamond 2005:109).

Little effort was required to raise crops on Easter island. This allowed for the development of a sophisticated social structure. Clans were led by chiefs and competed with each other. Among their competitions were the construction of ahus, or ceremonial areas with large statues. These immense statues required alarming amounts of resources to move. Timber was in fact the only resource available for this effort, and the islanders ingeniously discovered that sliding timber tracks would enable them to move these statues. It turns out this discovery accelerated their downfall (Ponting 1993). Because timber was necessary not just for social functions but also for heating and shelter, conditions became primitive almost overnight when the last trees were cut down.

Our current situation is much like that of Easter Island at the height of its civilization. We spend most of our time on leisure activities, and relatively little on procuring food. We spend this leisure time engaged in activities which are quickly depleting the environment. Travelling, eating in restaurants, and producing large amounts of trash are all taking a toll. We can expect that the decline of our civilzation will take longer only because the whole earth is so much larger than Easter island. (You can focus on the activities we do that directly impact the Amazon rainforest.)

What could have been done to prevent the downfall of Easter Island? In such a small area, it would be essential not to cut down more trees than could be regrown quickly. This is a lesson in sustainable development. The Amazon rainforest shows us just how difficult it is to prevent people from using lumber. The rainforest seems like an endless bounty to the loggers and farmers of Brazil. But at its current rate of destruction, it will last only until 2050 (Turner 2001). Deforestation is an environmental disaster that does not remedy itself in human lifetimes. Erosion follows, making it difficult for new vegetation to establish a foothold.

According to this New York Times Article (http://geog.tamu.edu/~cbrannst/Geog323/EnvConservation/Amazon%20&%20GlobalWarming.pdf#search=%22climatic%20importance%20deforestation%20amazon%20jungle%22)
the Amazon rainforest could play a critical role in global climate. Thus, its destruction will not be the downfall of only Brazilian farmers, but of every nation.

References

Diamond, Jared 2003. Collapse: How Societies Choose to Fail or Succeed. Penguin Books ISBN 0143036556. Chapter 2: Twilight at Easter pp.79-119.

Ponting, Clive 1993. A Green History of the World: The Environment and the Collapse of Great Civilizations. Penguin Books.

Turner, I.M. 2001. The ecology of trees in the tropical rain forest. Cambridge University Press, Cambridge. ISBN 0521801834

It isn't clear from your assignment if you are to discuss sustainable development in other nations, or just in terms of Brazil and the rain forest. There is much to say about how other nations could play a role in sustainable development in both situations. For example here is a link to information about a boycott of soy grown in Brazil (http://www.buzzle.com/editorials/7-23-2006-103269.asp). Sustainable development is a vast topic; just look at this list of web sites that has been compiled:
http://www.ulb.ac.be/ceese/meta/sustvl.html