After gradual declension down to about 39 hours in 1970, the workweek in the United States has steadily increased to the point that the average worker now puts in an estimated 164 extra hours of paid labor a year

(A) After gradual declension down

(B) Following a gradual declension down

(C) After gradual declining down

(D) After gradually declining

(E) Following gradually declining

I know that someone has asked this problem previously, but I have a different question about the explanation.

The explanation for E in OG is "Phrase MUST be introduced by a preposition(after), not a participle(following)".

Then, how come this sentence is correct?

Using accounts of various ancient writers, scholars have painted a sketchy picture of the activities of an all-female cult that, perhaps as early as the sixth century BC, worshiped a goddess known in Latin as Bona Dea, " the godess."

"accounts of various ancient writers" is a phrase, right? Then, according to the explanation above, "accounts of various ancient writers" should be introduced by a preposition then.

Am I missing something?

Thanks in advance.

The key in the first question is that "Following gradually declining" pairs a participle (which ends in -ing) with a gerund (which also ends in -ing). Two -ing's in a row is a no-no.

The second example you gave does not include a gerund. The OG explanation didn't actually explain why this particular phrase required a preposition instead of a participle.