To find how many times higher the number of library visits before examination day is compared to the average number of visits, you can divide the two quantities:
- Number of visits before examination day: \( 2 \times 10^3 = 2000 \)
- Average number of visits: \( 5 \times 10^2 = 500 \)
Now, divide the number of visits before examination day by the average number of visits:
\[ \frac{2000}{500} = 4 \]
Therefore, the number of library visits before examination day is 4 times higher than the library visits in an average week.