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claude wants to buy a car and there are a few factors that will affect the decision he makes in choosing what car he should buy. the first factor that can affect his decision regarding what car to buy can be the social and the cultural influence of the society he is living in. for example, there might be a certain car that might have a better value in the eyes of the society or in other words a better social norm regarding that car.

another factor can be personal habits. claude might need a spacious car because he might have kids or might utilize the back seat for other purposes hence a sports car (2 seated) won’t be appropriate.  

to answer your question:

f(x)= a^x.  if x=0, f(x)=1  if x=1, f(x)=a  if x=1, f(x)=a^a