The more interesting use of "age" is our English word "eon" translated from the Greek "aion". This is a particular period of history mentioned previously.

Greek Strong's #165 aion ahee-ohn' from the same as 104; properly, an age; by extension, perpetuity (also past); by implication, the world; specially (Jewish) a Messianic period (present or future):--age, course, eternal, (for) ever(-more), (n-)ever, (beginning of the , while the) world (began, without end). Compare 5550. Strongs Bible Dictionary

The Hebrew equivalent is:
5769 `owlam o-lawm' or lolam {o-lawm'}; from 5956; properly, concealed, i.e. the vanishing point; generally, time out of mind (past or future), i.e. (practically) eternity; frequentatively, adverbial (especially with prepositional prefix) always:--alway(-s), ancient (time), any more, continuance, eternal, (for, (n-))ever(-lasting, -more, of old), lasting, long (time), (of) old (time), perpetual, at any time, (beginning of the) world (+ without end). Compare 5331, 5703. Strongs Bible Dictionary

Unfortunately, "aion" is frequently (mis)translated as "world" "ever" or "eternity". Many times "for ever" or "for eternity" only mean "for the age". Knowing this "for ever and ever" means "for two ages" and "for ever" means "for the age". (see The End of "Eternity")

Below, we can see how some Bibles translate correctly:

Titus 2:12 KJV
Teaching us that, denying ungodliness and worldly lusts, we should live soberly, righteously, and godly, in this present world;

Titus 2:12 - Young's Literal Translation (1898)
teaching us, that denying the impiety and the worldly desires, soberly and righteously and piously we may live in the present age,

Hebrews 6:5 KJV
And have tasted the good word of God, and the powers of the world to come,

Hebrews 6:5 - The Emphasised Bible by J. B. Rotherham
And have tasted God's utterance to be, sweet, mighty works also of a coming age,

Hebrews 6:5 - Restored name
And have tasted the good word of יהוה (Yahweh, ou god], and the powers of the world to come,

Hebrews 6:5 - Young's Literal Translation (1898)
and did taste the good saying of God, the powers also of the coming age,

1 Corinthians 1:20 the King James Version reads:
Where is the wise? where is the scribe? where is the disputer of this World? hath not God made foolish the wisdom of this world?

The word "world" appears twice in this paragraph. Upon comparing this scripture with the Greek manuscripts we find that the last "world" is correct, coming down from the Greek word KOSMOS. Now if the King James translators are consistent, we will find the first "world" in this paragraph to be KOSMOS also. This is not the case. The first "world" in the Greek is "AION". This is a classic example of inconsistency of bringing down from two different Greek words into one and the same English word. The reverse is also true.

"AGE" never denotes eternity, endlessness, time without end, perpetuity of time, unending or unlimited duration. We now have arrived at the true definition of the word AGE. AGE is a duration of time having a beginning and an end. The duration of this time differs with the context of the scripture it is used in. AIONION the adjective modifies its noun AION or AGE and means lasting during the AGE, or AGE LASTING.

AION or AGE = a limited duration of time
AIONIOS or AGE-LASTING = lasting during the age

See a concordance of the Greek noun AION and its adjective AIONIOS with their deviations for your reference in your studies.