What should Dr. Carter do after receiving an email with a question he cannot answer quickly?

The most appropriate action for Dr. Carter to take after receiving an email with a question he cannot quickly answer is to communicate with the sender within 24 hours to inform her of the delay. This approach demonstrates professionalism and acknowledges the sender’s inquiry. By providing timely communication, Dr. Carter shows he values the sender's question and appreciates the importance of providing a clear and informed response. It also sets clear expectations regarding when additional information will be available, thereby maintaining a good relationship and ensuring that the sender does not feel ignored or neglected.

The other choices would not be suitable. Ignoring the email would leave the sender uncertain and frustrated, while offering a vague answer could lead to misunderstanding or additional confusion. Letting the sender know he will respond next month is excessively delayed and does not provide the courtesy of prompt communication, which is crucial in professional interactions.