anwachsen
to increase
To increase in amount, number, extent, or intensity; to become larger.
Der Schuldenberg ist auf eine beachtliche Summe angewachsen.
The mountain of debt has increased to a considerable sum.

to grow / increase
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to increase
To increase in amount, number, extent, or intensity; to become larger.
Der Schuldenberg ist auf eine beachtliche Summe angewachsen.
The mountain of debt has increased to a considerable sum.

'Anwachsen' (to grow/increase) is a separable verb. The prefix 'an-' appears at the end in main clauses. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Druck auf die Regierung wächst täglich an.
The pressure on the government is increasing daily.
The perfect tense of 'anwachsen' (to grow/increase) is always formed with the auxiliary verb 'sein' (to be), because it describes a change of state or growth. So the correct form is 'ist angewachsen' (has grown/has increased).
Die Bevölkerung der Stadt ist im letzten Jahr stark angewachsen.
The population of the city increased sharply last year.
When the result of the growth is a specific number or amount, the preposition 'auf' is used followed by the accusative.
Das Vermögen des Unternehmens ist auf über eine Milliarde Euro angewachsen.
The company's assets have increased to over one billion euros.
This meaning is used in gardening and botany. It describes whether a plant successfully takes root in a new place. It is often combined with adverbs like 'gut' (well) or 'schlecht' (poorly).
Die frisch gepflanzten Rosen sind gut angewachsen.
The freshly planted roses have taken root well.
In this meaning, the verb describes a firm, physical connection with a surface. It is almost always used with the preposition 'an' and the dative to name this surface.
Die Muscheln sind fest am Schiffsrumpf angewachsen.
The mussels have grown firmly onto the ship's hull.
to rise / climb
'steigen' and 'anwachsen' can both mean that an amount, number, or intensity becomes greater. 'steigen' is very general and fits especially well with prices, temperatures, numbers, or a level. 'anwachsen' emphasizes more strongly that something becomes larger or more extensive over time, for example a group, a problem, or an amount of work. Learners may confuse the words because both express an increase. As a practical rule: for short, clear statements like 'die Preise steigen' (prices are rising), 'steigen' is more natural; when something is slowly becoming larger, 'anwachsen' often sounds more precise.

Durch die vielen neuen Aufgaben wächst der Druck im Team weiter an.
Because of the many new tasks, the pressure on the team continues to grow.
Die Mieten in der Stadt steigen jedes Jahr.
Rents in the city rise every year.