Final answer:
The best synonyms for 'exemplary' are 'outstanding' or 'model' when referring to literacy programs recognized for their high quality, and 'illustrative' or 'representative' for essays that are so good that they should be followed as an example.
Step-by-step explanation:
When choosing the best synonym for exemplary in the given sentences, one must consider the context in which the word is used in order to select the most fitting alternative. The first sentence, 'The library has received public recognition for its exemplary literacy programs,' suggests that the literacy programs are of such high quality that they serve as a model for others. Therefore, a suitable synonym here could be 'outstanding' or 'model.' In the second sentence, 'If you are not sure how to format your paper, look at the exemplary essays that the teacher handed out,' the term indicates that the essays are so good that they should be used as an example for others to follow. A fitting synonym for this usage could be 'illustrative' or 'representative.'