Explanation

Creating a filter: in the original sentence, the relative pronoun "that" should be "whom," since artists are people. That inaccuracy may not be a decisive defect, however. To improve the phrasing, I'd omit a couple words through elision without loss of clarity and say, "tend to back artists they expect to gain...," which is perfectly grammatical. We can use this prediction of the correct answer as our filter.

Applying the filter: scanning down, we can see that our prediction is quite similar to answer choice (C). Choices (B) and (E) use "they" in a new independent clause that could refer falsely to the producers, so those two are out. Choice (D) is missing a relative pronoun such as "who," and it uses a needless gerund, "being," at the beginning of the phrase. Reflecting back on (A), we can see that the future tense of "will gain popularity" lacks consistency of grammar and sense with the latter verb in "who are." The correct answer is (C).