d) If the temperature of the background radiation today is  at what time after the birth of the universe was the temperature  Take the age of the universe as  years. 

To solve this problem, we need to use the relationship between the temperature of the cosmic background radiation and the scale factor of the universe, which is determined by the expansion of the universe.

The temperature of the cosmic background radiation is inversely proportional to the scale factor of the universe, which is related to the age of the universe. We can express this relationship as:

T ∝ 1/a

Where:
- T is the temperature of the cosmic background radiation
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