
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.

ascent
A path, road, or terrain that leads upward; an incline.
Der Anstieg zum Gipfel des Berges war sehr anstrengend.
The ascent to the mountain summit was very strenuous.
'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.
ascent / rise
Aufstieg refers to movement upward, whereas Anstieg refers to a path or terrain that leads upward. On a mountain hike, Aufstieg is therefore the action, while Anstieg is the uphill section of the route.

Der steile Anstieg zum Gipfel begann direkt hinter der Hütte.
The steep climb to the summit began just behind the hut.
Der Aufstieg zum Gipfel dauerte fast drei Stunden.
The ascent to the summit took almost three hours.