To find out how many times higher the number of library visits before examination day is compared to the average weekly visits, we first need to understand the figures given:
- Total visits in two weeks: \(2 \times 10^3 = 2000\)
- Average visits in one week: \(5 \times 10^2 = 500\)
Now, since the librarian monitored the number of visits over a two-week period, we can compute the average visits per week for that period:
\[ \text{Average visits per week during two weeks} = \frac{2000 \text{ visits}}{2 \text{ weeks}} = 1000 \text{ visits/week} \]
Now, we need to compare this with the average visits:
- Average visits in an average week: \(500\)
Next, we find how many times higher the visits were during the two-week period compared to the average visits in one week:
\[ \text{Number of times higher} = \frac{\text{Average visits during two weeks}}{\text{Average visits in one week}} = \frac{1000}{500} = 2 \]
So, the number of library visits before examination day is 2 times higher compared to the library visits in an average week.
Thus, the answer is:
2 times.