Give an example of final causality in human action and in the action of non-rational animals. Is it reasonable today to assert that final causality is also present in the activity of inanimate things?

Final causality refers to Aristotle’s theory of the four causes. These are four types of explanations of change or movement. The fourth cause is the end or purpose (telos), that for the sake of which a thing exists or is done. According to Aristotle, a seed has as its end to become an adult plant. In human action, the final causality of a man walking could be to stay fit. In the animal world, the final causality of a dog barking could be to scare away a potential threat.  
Some mistakenly believe Aristotle’s theory of final causality reads human purposes and intentions into the natural world. Rather, this teleological view of the natural world means that whatever lies at the end of the typical developmental changes of a species is its final causality.
In scientific fields, teleological explanations have gone out of favor and are often deliberately avoided because conclusions about final and formal causation are often faulty or subjective. Instead, scientific explanations tend to focus more on material and efficient explanations. In evolutionary biology, however, teleological language is still used to describe natural tendencies toward particular end conditions.
Regarding final causality in the activity of inanimate things, this view can still be regarded as reasonable because it does not posit that inanimate things have a consciousness of purpose. Rather, an inanimate process can have a final purpose. For example, rain falling to the earth is not consciously aware of its purpose but still serves the final purpose of hydrating plants.