To find how many times higher the number of library visits before examination day is compared to the average week, we need to divide the total visits during the two-week period by the average number of visits in one week.
The total visits during the two-week period is given as \(2 \times 10^3\), which is equal to \(2000\).
The average visits in one week is given as \(5 \times 10^2\), which is equal to \(500\).
Now, we calculate the number of times higher:
\[ \text{Number of times higher} = \frac{2000}{500} = 4 \]
So, the number of library visits before examination day is 4 times higher than the library visits in an average week.