To find out how many times higher the number of library visits before examination day is compared to the average week, we will divide the number of visits during the one-week period by the number of visits in an average week.
Number of visits during the examination week: \( 2 \times 10^3 = 2000 \)
Number of visits during an average week: \( 5 \times 10^2 = 500 \)
Now, we perform the division:
\[ \frac{2000}{500} = 4 \]
Therefore, the number of library visits before examination day is 4 times higher than the number of visits in an average week.