der Anstieg
increase
A rise or increase in numbers, values, prices, or temperatures.
Die Firma verzeichnete einen deutlichen Anstieg des Gewinns im letzten Quartal.
The company recorded a significant increase in profit last quarter.

increase / ascent
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increase
A rise or increase in numbers, values, prices, or temperatures.
Die Firma verzeichnete einen deutlichen Anstieg des Gewinns im letzten Quartal.
The company recorded a significant increase in profit last quarter.

'Der Anstieg' (the increase/ascent) is the nominalization of the verb 'ansteigen' (to rise/increase). The prefix 'an-' here indicates an upward movement or an increase, which explains both meanings of the noun.
Die Preise für Energie steigen weiter an.
Energy prices continue to rise.
You can recognize the meaning from the context: if it is about numbers, data, or values (prices, temperatures, stocks), it means an increase. If it is about a path, mountain, or road, it means an incline or ascent.
Der Anstieg der Arbeitslosenzahlen bereitet Sorgen.
The increase in unemployment figures is causing concern.
When referring to an increase in values, the prepositions 'von' (of/in) or 'um' (by) are often used. 'Anstieg von' names the thing that is increasing, while 'Anstieg um' gives the specific amount of the increase.
Wir beobachten einen Anstieg von 10 Prozent.
We are observing an increase of 10 percent.
growth
'das Wachstum' and 'der Anstieg' both describe that something is becoming more. However, 'Wachstum' fits better for a development over a certain period of time, for example with a company, an economy, or an idea. 'Anstieg' is used especially for numbers, prices, temperatures, or values. Learners may confuse the words because both mean an increase. As a guide: if you are talking about a value that is becoming higher, 'Anstieg' often sounds more precise. If you mean the development of something larger or more long-term, 'Wachstum' is more natural.

Der Anstieg der Mieten macht vielen Familien Sorgen.
The increase in rents is worrying many families.
Das Wachstum der kleinen Firma war in diesem Jahr stärker als erwartet.
The small company's growth was stronger than expected this year.