erheblich
considerable
To a large or important extent; substantial, significant.
Die neuen Maßnahmen haben zu einer erheblichen Verbesserung der Situation geführt.
The new measures have led to a considerable improvement in the situation.

considerable
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considerable
To a large or important extent; substantial, significant.
Die neuen Maßnahmen haben zu einer erheblichen Verbesserung der Situation geführt.
The new measures have led to a considerable improvement in the situation.

The word 'erheblich' (considerable) is related to the verb 'erheben' (to raise), which means 'anheben' (to lift) or 'emporheben' (to raise up). Something that is 'erheblich' is therefore 'raised beyond' the normal level and thus significant.
Der Sturm verursachte erhebliche Schäden am Dach.
The storm caused considerable damage to the roof.
'Erheblich' can stand before a noun as an adjective or modify a verb or another adjective as an adverb. As an adverb, it remains unchanged.
Es gibt einen erheblichen Preisunterschied.
There is a considerable price difference.
'Erheblich' is often used to describe the extent of abstract things. Common combinations include 'erhebliche Zweifel' (considerable doubts), 'erhebliche Kosten' (considerable costs), 'ein erheblicher Teil' (a considerable part), or 'erheblicher Einfluss' (considerable influence).
Die Reform hatte einen erheblichen Einfluss auf die Wirtschaft.
The reform had a considerable influence on the economy.
This word belongs more to written language and more formal contexts. You often find it in news, reports, and specialist texts.
Die Untersuchung ergab erhebliche Mängel bei der Sicherheit.
The investigation revealed considerable safety deficiencies.
much / a lot
'viel' and 'erheblich' can both show that a difference or extent is large. 'viel' is the simple and very common word, especially in everyday comparisons like 'viel teurer' (much more expensive) or 'viel schneller' (much faster). 'erheblich' sounds more factual and stronger; it fits well when a difference is important or clearly measurable. In normal conversation, people often say 'viel'. In news reports, reports, or official texts, 'erheblich' sounds more natural.

Durch den neuen Plan spart die Familie erheblich mehr Geld.
With the new plan, the family saves considerably more money.
Heute kostet der Eintritt viel mehr als letztes Jahr.
Today admission costs much more than last year.