Evaluate the extent to which exploration changed in relation to the growth of european nations and the desire to trade.
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I assume the time period the question is referring to is the period between 1492 and ~1800.

In terms of trade:

In the late 15th century, the economy of the nations of Europe began expanding massively, and as people become wealthier, so did the demand for imported goods expand. In particular, the wealthy classes of Europe fueled a massive demand for spices, which were imported from Asia as they could not be grown in Europe's harsh and cold climate. In general, these spices would be imported to Europe over land routes (the most famous of which was the silk road). Unfortunately, these routes were not very dependable, as they were slow, filled with thieves, and passed through the emergent Ottoman Empire (with which the Western Europeans had incredibly poor relations). As a result, the need to find alternate routes of trade became a pressing issue for Western European governments.

Western European nations, particularly Spain and Portugal, began funding exploratory expeditions to find sea routes to Asia. The most important of these exploratory missions was undertaken by Christopher Columbus in 1492, when he sailed west out into the Atlantic instead of South around Africa as his Portuguese predecessors had. Christopher Columbus accidentally discovered the Americas, and his discovery caused a European scramble to control the so called "New World" and its riches.

In terms of growth (assuming this means population growth):

During the 15th - 18th centuries, Europe experienced a population explosion as medical science progressed rapidly during the Renaissance and Enlightenment periods, reducing mortality. As a result of this explosion, many countries began to have their populations grow wildly out of control. These European nations needed a place for their populace to migrate to, to alleviate their burden on the state. The New World provided a convenient solution to this, as it was sparsely inhabited (with the exception of Mesoamerica and Peru) and incredibly resource rich. Because of this, European governments funded exploratory expeditions to find potential locations to establish colonies during this period.