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An essay that examines the destructive nature of hurricanes over the past decades is an example of EXPOSITORY ESSAY.
An expository essay is an organized piece of writing which explains a specific topic to a defined audience. An expository essay is typically make up of an introductory paragraph, which consist of the thesis statement, the supporting paragraphs and the conclusion. 

an essay that examines destructive nature of hurricanes over the past decade is an example of which kind of essay?

An essay that examines the destructive nature of hurricanes over the past decades is an example of EXPOSITORY ESSAY