exponential
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exponential
Describes growth or an increase that accelerates faster and faster. Something increases disproportionately strongly.
Die Zahl der Infektionen stieg exponentiell an.
The number of infections increased exponentially.
The adjective 'exponentiell' (exponential) is derived from the noun 'der Exponent' (the exponent in mathematics). It describes growth that is as strong as in exponentiation.
Das exponentielle Wachstum der Stadtbevölkerung führt zu neuen Herausforderungen.
The exponential growth of the urban population is creating new challenges.
In its general meaning, 'exponentiell' (exponential) is almost always combined with verbs of change, for example 'exponentiell wachsen' (to grow exponentially), 'exponentiell ansteigen' (to rise exponentially), or 'exponentiell zunehmen' (to increase exponentially).
Die Nutzung von sozialen Medien ist in den letzten Jahren exponentiell gewachsen.
The use of social media has grown exponentially in recent years.
'Exponentiell' (exponentially) is very often used as an adverb to describe the manner of an increase. It then remains unchanged in the sentence and refers to the verb.
Die Datenmenge im Internet wächst exponentiell.
The amount of data on the internet is growing exponentially.
You can recognize the purely mathematical meaning from the context. When 'Funktion' (function), 'Gleichung' (equation), or 'Kurve' (curve) is mentioned, the technical meaning is usually intended.
Im Unterricht analysieren wir heute die Eigenschaften der exponentiellen Gleichung.
In class today, we are analyzing the properties of the exponential equation.
linear
'linear' and 'exponentiell' are both often used when describing growth, numbers, or curves. For that reason, learners can easily confuse them. 'Linear' means that something increases evenly, for example always by the same amount. The graph is then a straight line. 'Exponentiell' means that something grows faster and faster, often because it keeps multiplying. The difference is practically important: linear growth is steady and regular, while exponential growth may be slow at first but becomes very strong later.
Die Zahl der Nutzer wuchs exponentiell, nachdem die App bekannt wurde.
The number of users grew exponentially after the app became well known.
Die Kosten steigen linear, weil jede zusätzliche Stunde gleich viel kostet.
The costs increase linearly because each additional hour costs the same amount.