Explanation:

Correct answer is (e). In option A, ‘acknowledging’ would be a correct choice but the word 'efforts' would be wrong here. Efforts can decrease, efforts can lessen but 'efforts faded' is something we don't use often. This eliminates option A.
Option B gets eliminated as well as the word 'executing' for the second blank doesn't fit in the context of the passage. 
Option C would have been correct had the word for the first blank been 'enthusiasm' instead of 'enthusiastic'.
In option D, the word 'placating' which means 'to make (someone) less angry or hostile' would be absurd in the given context of the passage.
In option E, the word 'alacrity' which refers to 'brisk and cheerful readiness' and the word 'realizing' which means 'to get to know or understand something' fit the first and the second blank respectively and most appropriately.
Option E is hence the correct answer.