der Zuwachs
increase
An increase in amount, number, size, or value; growth.
Das Unternehmen verzeichnete im letzten Quartal einen deutlichen Zuwachs an Kunden.
The company recorded a significant increase in customers last quarter.

increase / addition
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increase
An increase in amount, number, size, or value; growth.
Das Unternehmen verzeichnete im letzten Quartal einen deutlichen Zuwachs an Kunden.
The company recorded a significant increase in customers last quarter.

'Der Zuwachs' is derived from the verb 'zuwachsen' (to increase/grow). The prefix 'zu-' signals an addition or increase, which explains the meaning 'growth' or 'rise'.
Die Schulden sind im letzten Jahr stark zugewachsen.
The debts increased sharply last year.
To express the area in which something is increasing, the preposition 'an' is used followed by the dative. This pattern is very common.
Wir verzeichnen einen Zuwachs an neuen Mitgliedern.
We are recording an increase in new members.
In a family context, 'Zuwachs' is often used as a friendly way to refer to the birth of a baby. The phrase 'Zuwachs bekommen' (to have a new addition) is very typical for this.
Unsere Nachbarn haben letzten Monat Zuwachs bekommen.
Our neighbors had a new addition last month.
growth
'das Wachstum' and 'der Zuwachs' both have to do with an increase. 'Wachstum' often describes the process: something becomes bigger, stronger, or develops further. This can refer to plants, companies, or ideas. 'Zuwachs' is more about what has been added, meaning the additional amount, number, or even new people in a group. That is why they can sometimes be confused when talking about numbers. If you mean the development over time, 'Wachstum' is more natural. If you mean the plus or new members, 'Zuwachs' fits better.

Der Verein freut sich über den Zuwachs von fünf neuen Mitgliedern.
The club is pleased about the addition of five new members.
Wegen der guten Pflege war das Wachstum der Pflanzen im Sommer sehr stark.
Because of the good care, the plants' growth was very strong in the summer.