Select the option with the correct use of future tense.

To express an action, state, or event that is expected to happen or be completed in the future (indicated here by the time phrase "by next week"), we use the simple future tense.

The correct form of the simple future tense is constructed using the auxiliary verb will followed by the base form of the main verb (will + get).

Let's analyze the given options:

1. "I hope your health is getting better by next week." – Uses present continuous tense ("is getting"), which is incorrect for a simple future expectation with a specific future timeframe.

2. "I hope your health will get better by next week." – Uses the simple future tense ("will get"), which correctly indicates a future prediction/hope.

3. "I hope your health have been getting better by next week." – Grammatically incorrect subject-verb agreement ("health" is singular and takes "has", not "have") and improper use of present perfect continuous tense.

4. "I hope your health is get better by next week." – Grammatically incorrect structure ("is get").

Therefore, the correct answer is "I hope your health will get better by next week."