Binary Search Symbol Table

Hi I'm attempting to self teach myself from Algorithms (Sedgewick) and ran across the following problem:

3.1.15: Assume that searches are 1,000 times more frequent
than insertions for a BinarySearchST client. Estimate the
percentage of the total time that is devoted to insertions,
when the number of searches is 10^3, 10^6, and 10^9.

As stated in the problem Searches (S) = 1000 * Inserts (I)

• $$S = 10^3 \to I = 1$$
• $$S = 10^6 \to I = 10^3$$
• $$S = 10^9 \to I = 10^6$$

At this point in the book we are using simple arrays and linked lists to back symbol table (not efficient hash maps, trees, etc). This would mean searches take ~log2(N) time and insertions take ~N/2 time (assuming a uniform distribution on where inserts are placed).

Am I correct in calculating the % of insert to search time would approximately be:

$$\frac{Inserts \times N/2}{Searches \times \log_2(N)}$$

Using $$Searches = 10^3 \times Inserts$$ this reduces to

$$\frac{N/2}{(10^3 \times log_2(N)}$$

This would mean the percentage depends heavily on the initial size of the symbol table and is not a steady percentage that we can use to answer the question.

Any suggestions for what I am overlooking, should I be making an assumption about the initial size of the table? 