Professor stewart wrote a very positive letter of recommendation for a student despite having doubts about her competence. which theory best explains why he subsequently began to develop more favorable attitudes about the student's abilities?

cognitive dissonance theory  

Explanation:

Cognitive dissonance theory was proposed by Leon Festinger in 1957 and this theory explains the relationships between cognitions. There is a tendency for an individual to see their cognition in a consistent manner such as belief, opinion. If there is found any inconsistency between behavior and attitudes(dissonance) something must change to eliminate the dissonance between attitude and behavior( dissonance). If there is happening something discrepancy between behavior and attitude then attitudes will change to accommodate the behavior.  

There are two factors which affect the dissonance:

b) to encourage free trade

answer; no longer than a reasonable period of time;