
zurückgehen
to go back
To return to a place one came from.
Nach dem Spaziergang gehen wir wieder nach Hause zurück.
After the walk, we'll go back home.
to go back / decline
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to go back
To return to a place one came from.
Nach dem Spaziergang gehen wir wieder nach Hause zurück.
After the walk, we'll go back home.

to decline
To become less; to decrease in quantity, value, or intensity.
Die Verkaufszahlen sind im letzten Quartal stark zurückgegangen.
The sales figures declined sharply in the last quarter.

to go back to
To have one's origin or cause in something.
Viele moderne Traditionen gehen auf alte Bräuche zurück.
Many modern traditions go back to old customs.
'Zurückgehen' (to go back/decline) is a separable verb. The prefix 'zurück-' stands at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Wann gehst du heute Abend nach Hause zurück?
When are you going back home tonight?
Since 'zurückgehen' (to go back/decline) describes movement, the perfect tense is always formed with the auxiliary verb 'sein' (to be), not with 'haben' (to have).
Die Touristengruppe ist bereits zum Bus zurückgegangen.
The tourist group has already gone back to the bus.
In the meaning 'to have its origin', 'zurückgehen' (to go back to) is always used with the preposition 'auf' and the accusative. This structure is fixed.
Der Name der Stadt geht auf einen römischen Kaiser zurück.
The name of the city goes back to a Roman emperor.
When 'zurückgehen' (to decline) means 'to decrease' or 'to become less', the subject is often an abstract quantity. Typical examples are numbers, prices, interest, or temperature.
Die Arbeitslosigkeit ist in diesem Jahr leicht zurückgegangen.
Unemployment has declined slightly this year.
to sink / fall
For prices, amounts, or levels, sinken and zurückgehen are often both possible. sinken puts more emphasis on the lower measurable level, while zurückgehen refers more generally to a decrease. sinken is especially suitable when an exact figure is given; zurückgehen is a natural choice for a general trend.

Der Preis für das Ticket ging im Mai deutlich zurück.
The ticket price declined significantly in May.
Der Preis für das Ticket sank im Mai auf 20 Euro.
The ticket price fell to 20 euros in May.